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Solve one-step and two-step equations: word problems

Which recursive formula can be used to define this sequence for

n>1

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\begin{array}{l} -4,3,10,17,24,31, \ldots \\ a_{n}=a_{n-1}+a_{n-2}+7 \\ a_{n}=-\frac{3}{4} a_{n-1} \\ a_{n}=a_{n-1}+7 \\ a_{n}=a_{n-1}+a_{n-2}-7 \end{array}

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1

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\begin{array}{l} f(t)=t^{2}-10 t \\ h(t)=\frac{24}{t} \end{array}

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Vince tried to evaluate

f(h(12))

, but he made a mistake. Here is his work.

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1 \quad f(12)=12^{2}-10(12)

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=24

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2

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\begin{aligned} h(24) & =\frac{24}{24} \\ & =1 \end{aligned}

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3 f(h(12))=1

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What is the mistake in Vince's work?

After begging his parents for

3

years, Garrett is finally going to clown college! On the first day, his juggling instructor divides a box of bean bags equally among the

17

clowns in Garrett's class. Each clown gets

4

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Which equation can you use to find the number of bean bags

b

in the instructor's box?

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b - 17 = 4

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17b = 4

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\frac{b}{17} = 4

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b + 17 = 4

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Solve this equation for

b

to find the number of bean bags in the instructor's box.

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z

is a solution to this equation?

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7z=63

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z=7

z=9

On a rainy day, Eva and her friends play a marble game called Revenge. To start, Eva divides a bag of marbles evenly among the

6

players. Each player gets

13

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Which equation can you use to find the number of marbles

m

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\frac{m}{6} = 13

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m + 6 = 13

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m - 6 = 13

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6m = 13

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Solve this equation for

m

to find the number of marbles in the bag.

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On a rainy day, Kimi and her friends play a marble game called Revenge. To start, Kimi divides a bag of marbles evenly among the

6

players. Each player gets

13

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Which equation can you use to find the number of marbles

m

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6m = 13

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\frac{m}{6} = 13

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m + 6 = 13

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m - 6 = 13

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Solve this equation for

m

to find the number of marbles in the bag.

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Isabelle won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Isabelle a bucket of fish to divide evenly among

5

dolphins. Each dolphin gets

4

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Which equation can you use to find the number of fish

f

in the bucket before Isabelle feeds the dolphins?

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f + 5 = 4

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f - 5 = 4

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5f = 4

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f/5 = 4

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Solve this equation for

f

to find the number of fish in the bucket before Isabelle feeds the dolphins.

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Based on the following calculator output, determine the population standard deviation of the dataset, rounding to the nearest

1

ooth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=238.428571429 \\ \Sigma x=1669 \\ \Sigma x^{2}=399997 \\ S x=18.5279711325 \\ \sigma x=17.1535680824 \\ n=7 \\ \min \mathrm{X}=216 \\ \mathrm{Q}_{1}=224 \\ \mathrm{Med}^{2}=234 \\ \mathrm{Q}_{3}=254 \\ \max \mathrm{X}=271 \end{array}

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Based on the following calculator output, determine the population standard deviation of the dataset, rounding to the nearest

1

ooth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=106 \\ \Sigma x=742 \\ \Sigma x^{2}=80706 \\ S x=18.5022521152 \\ \sigma x=17.1297568993 \\ n=7 \\ \operatorname{minX}=81 \\ \mathrm{Q}_{1}=87 \\ \mathrm{Med}^{2}=113 \\ \mathrm{Q}_{3}=121 \\ \max \mathrm{X}=126 \end{array}

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Based on the following calculator output, determine the mean of the dataset, rounding to the nearest

10

oth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=137.142857143 \\ \Sigma x=960 \\ \Sigma x^{2}=132126 \\ S x=8.83984485966 \\ \sigma x=8.18410604994 \\ n=7 \\ \operatorname{minX}=128 \\ \mathrm{Q}_{1}=129 \\ \mathrm{Med}^{2}=137 \\ \mathrm{Q}_{3}=149 \\ \max \mathrm{X}=149 \end{array}

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Based on the following calculator output, determine the inter-quartile range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=244.857142857 \\ \Sigma x=1714 \\ \Sigma x^{2}=421554 \\ S x=17.6486880667 \\ \sigma x=16.3395101468 \\ n=7 \\ \operatorname{minX}=220 \\ \mathrm{Q}_{1}=232 \\ \mathrm{Med}^{2}=240 \\ \mathrm{Q}_{3}=265 \\ \operatorname{maxX}=269 \end{array}

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Based on the following calculator output, determine the range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=106.714285714 \\ \Sigma x=747 \\ \Sigma x^{2}=89485 \\ S x=40.3514323815 \\ \sigma x=37.3581671534 \\ n=7 \\ \operatorname{minX}=54 \\ Q_{1}=82 \\ \mathrm{Med}^{2}=102 \\ \mathrm{Q}_{3}=122 \\ \max \mathrm{X}=182 \end{array}

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Based on the following calculator output, determine the mean of the dataset, rounding to the nearest

10

oth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=213.285714286 \\ \Sigma x=1493 \\ \Sigma x^{2}=322787 \\ S x=26.9302449903 \\ \sigma x=24.9325621038 \\ n=7 \\ \operatorname{minX}=185 \\ \mathrm{Q}_{1}=200 \\ \mathrm{Med}^{2}=205 \\ \mathrm{Q}_{3}=228 \\ \max \mathrm{X}=267 \end{array}

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Based on the following calculator output, determine the inter-quartile range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=221.857142857 \\ \Sigma x=1553 \\ \Sigma x^{2}=356195 \\ S x=44.0659678642 \\ \sigma x=40.7971587646 \\ n=7 \\ \operatorname{minX}=167 \\ \mathrm{Q}_{1}=176 \\ \mathrm{Med}^{2}=232 \\ \mathrm{Q}_{3}=254 \\ \operatorname{maxX}=285 \end{array}

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Based on the following calculator output, determine the population standard deviation of the dataset, rounding to the nearest

1

ooth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=41.4285714286 \\ \Sigma x=290 \\ \Sigma x^{2}=12714 \\ S x=10.7990299388 \\ \sigma x=9.99795897538 \\ n=7 \\ \operatorname{minX}=27 \\ \mathrm{Q}_{1}=31 \\ \mathrm{Med}^{2}=41 \\ \mathrm{Q}_{3}=53 \\ \max \mathrm{X}=57 \end{array}

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Based on the following calculator output, determine the inter-quartile range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=239.428571429 \\ \Sigma x=1676 \\ \Sigma x^{2}=406076 \\ S x=28.2657457173 \\ \sigma x=26.1689955201 \\ n=7 \\ \operatorname{minX}=191 \\ \mathrm{Q}_{1}=232 \\ \mathrm{Med}^{2}=237 \\ \mathrm{Q}_{3}=251 \\ \max \mathrm{X}=286 \end{array}

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Based on the following calculator output, determine the population standard deviation of the dataset, rounding to the nearest

1

ooth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=270 \\ \Sigma x=1890 \\ \Sigma x^{2}=512150 \\ S x=17.5594229214 \\ \sigma x=16.2568666811 \\ n=7 \\ \operatorname{minX}=240 \\ \mathrm{Q}_{1}=257 \\ \mathrm{Med}^{2}=274 \\ \mathrm{Q}_{3}=282 \\ \max \mathrm{X}=291 \end{array}

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Based on the following calculator output, determine the mean of the dataset, rounding to the nearest

10

oth if necessary.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=277.285714286 \\ \Sigma x=1941 \\ \Sigma x^{2}=542345 \\ S x=26.2469952929 \\ \sigma x=24.2999958008 \\ n=7 \\ \operatorname{minX}=246 \\ \mathrm{Q}_{1}=246 \\ \mathrm{Med}^{2}=272 \\ \mathrm{Q}_{3}=305 \\ \max \mathrm{X}=308 \end{array}

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Based on the following calculator output, determine the range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=243 \\ \Sigma x=1701 \\ \Sigma x^{2}=437751 \\ S x=63.7808748764 \\ \sigma x=59.0496159417 \\ n=7 \\ \operatorname{minX}=169 \\ \mathrm{Q}_{1}=200 \\ \mathrm{Med}^{2}=230 \\ \mathrm{Q}_{3}=297 \\ \max \mathrm{X}=356 \end{array}

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Bella's Burgers sells burgers, fries, and milkshakes. Last month, Bella's Burgers sold

\$20,000

of burgers, which had associated variable costs of

\$8,000

\$10,000

of fries, which had associated variable costs of

\$4,000

\$5,000

worth of milkshakes, which had associated variable costs of

\$2,000

. Bella's Burgers had total fixed costs of

\$6,000

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What is Bella's company-wide break-even point?

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\$21,000

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\$15,000

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\$35,000

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\$10,000

Eva maintained an average speed of

35\,\text{mph}

m

hours of her road trip. For the next

n

hours of the trip, she drove at an average speed of

60\,\text{mph}

. Eva drove a total of

225

4.5

hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first

m

hours of the trip?

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1

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m+n=225

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35m+60n=4.5

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m+n=4.5

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35 m+60 n=225

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m+n=225

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60 m+35 n=4.5

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m+n=4.5

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60 m+35 n=225

Eva maintained an average speed of

35\,\text{mph}

m

hours of her road trip. For the next

n

hours of the trip, she drove at an average speed of

60\,\text{mph}

. Eva drove a total of

225

4.5

hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first

m

hours of the trip?

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1

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m+n=225

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35m+60n=4.5

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m+n=4.5

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35 m+60 n=225

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m+n=225

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60 m+35 n=4.5

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m+n=4.5

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60 m+35 n=225

Urpi was given this problem:

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b(t)

of the base of a square prism is decreasing at a rate of

7

kilometers per minute and the height

h(t)

of the prism is increasing at a rate of

10

kilometers per minute. At a certain instant

t_{0}

, the base's side is

4

kilometers and the height is

9

kilometers. What is the rate of change of the surface area

S(t)

of the prism at that instant?

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Which equation should Urpi use to solve the problem?

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1

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S(t)=6[b(t)]^{2}

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S(t)=[b(t)]^{3}

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S(t)=2[b(t)]^{2}+4 b(t) \cdot h(t)

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S(t)=[b(t)]^{2} \cdot h(t)