Resources

Resources

Choose two-step equations: word problems

Tomer owns a daycare center called Kidz Kare. One afternoon he collected the age of each person in Kidz Kare. The following histogram summarizes the data he collected. A histogram with a vertical axis labeled

\text{Number of people}

and a horizontal axis labeled

\text{Age in years}

0

25

, in increments of

5

. Bar heights are approximately as follows. From

0

5

3

5

10

2

10

15

3

15

20

1

20

25

1

[0] [1] [2] [3] [4] [5] [6] [0] [5] [10] [15] [20] [25] [\text{Number of people}] [\text{Age (in years)}]

Based on this data, what is a reasonable estimate of the probability that the next person to enter Kidz Kare is between

10

15

years old? Choose the best answer.

\newline

1

\newline

\frac{2}{10}

\frac{2}{10}

\newline

\frac{2}{7}

\frac{2}{7}

\newline

\frac{3}{10}

\frac{3}{10}

\newline

\frac{3}{7}

\frac{3}{7}

Rosa's family wants to switch cell phone plans. Cloud Line Cell Service is offering a one-time discount of

25

\$

for families that use multiple phones with their service. Rosa's family uses

4

phones, and the salesperson said the first month's payment, which includes the discount and the regular monthly rate for each phone, will be

71

\$

. Which equation can Rosa use to find

x

, the regular monthly rate for each phone?

\newline

\newline

25(x - 4) = 71

\newline

25x - 4 = 71

\newline

4x - 25 = 71

\newline

4(x - 25) = 71

Reggie works at Bright Bouquets flower shop. Yesterday, he made

4

centerpieces, which would normally use up an entire shipment of roses. In the shop's latest shipment,

12

roses were wilted, so Reggie couldn't use them. He used the remaining

36

roses in the centerpieces.

\newline

Which equation can you use to find how many roses,

x

, Reggie normally uses in a centerpiece?

\newline

\newline

12(x - 4) = 36

\newline

4x - 12 = 36

\newline

4(x - 12) = 36

\newline

12x - 4 = 36

Tommy and his friends are planning a trip to the Mega Vault trampoline park. The employee Tommy spoke to on the phone said the total cost for all

5

of them would be

85\$

. This includes a

3\$

fee added to each entrance ticket to cover the cost of a pair of grip socks.

\newline

Which equation can you use to find

c

, the cost of an entrance ticket?

\newline

\newline

3c + 5 = 85

\newline

5c + 3 = 85

\newline

5(c + 3) = 85

\newline

3(c + 5) = 85

Ling and her friends are planning a trip to the Misty Falls water park. The employee Ling spoke to on the phone said the total cost for all

4

of them would be

76\$

. This includes an entrance ticket and a

6\$

tube rental fee for each person.

\newline

Which equation can you use to find

c

, the cost of an entrance ticket?

\newline

\newline

6c + 4 = 76

\newline

6(c + 4) = 76

\newline

4(c + 6) = 76

\newline

4c + 6 = 76

The members of Starville High School's student council are planning this year's school carnival. For the raffle, they plan to order one roll of

100

golden tickets. For the carnival games, they plan to order red tickets that come in rolls of

250

. Based on last year's numbers, they plan to order a total of

1,600

\newline

Which equation can the student council use to find how many rolls of red tickets,

r

, they should order?

\newline

\newline

250(r + 100) = 1,600

\newline

100(r + 250) = 1,600

\newline

100r + 250 = 1,600

\newline

250r + 100 = 1,600

Kenji is selling tickets to his troop's scouting fair. He set a goal of selling a certain number of tickets each week for

8

8

weeks, he had sold

115

tickets, but he was still

21

tickets short of his goal.

\newline

Which equation can you use to find how many tickets,

t

, Kenji hoped to sell each week to reach his goal?

\newline

\newline

21(t - 8) = 115

\newline

8t - 21 = 115

\newline

8(t - 21) = 115

\newline

21t - 8 = 115

Kamal's family is leaving for Merry Mountain Resort once his parents get home from work on Friday. Their house is

627

miles from the resort. They plan to stop and spend the night at a hotel after

4

hours of driving, then complete the rest of the trip on the second day. Their average speed is

60

miles per hour.

\newline

Which equation can you use to find how long,

x

, they will drive on the second day?

\newline

\newline

60(x + 4) = 627

\newline

4x + 60 = 627

\newline

4(x + 60) = 627

\newline

60x + 4 = 627

Mrs. Jones is taking her family to Penguin Zone ice rink. The employee she spoke to on the phone said the total cost for all

6

of them would be

72

\$

. This includes the entrance ticket and the

4

\$

skate rental fee for each person.

\newline

Which equation can you use to find

c

, the cost of an entrance ticket?

\newline

\newline

4c + 6 = 72

\newline

6(c + 4) = 72

\newline

6c + 4 = 72

\newline

4(c + 6) = 72

Pinewood Academy's winter carnival is coming up, and Mr. Meyer is in charge of ordering the craft kits again. He knows he ordered

9

boxes of snowman kits last year but can't remember how many kits come in a box. He checks the records and finds that the school used

168

of the snowman kits last year and had

12

left over after the event.

\newline

Which equation can Mr. Meyer use to find how many snowman kits,

k

, come in each box?

\newline

\newline

9(k - 168) = 12

\newline

9k - 168 = 12

\newline

168(k - 9) = 12

\newline

168k - 9 = 12

Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered

12

large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by

2\$

. The total came to

192\$

. Which equation can you use to find the amount of money,

p

, Roman Rounds normally charges for a large pizza?

\newline

\newline

12(p - 2) = 192

\newline

2(p - 12) = 192

\newline

2p - 12 = 192

\newline

12p - 2 = 192

Switch Gears Activity Boxes sends a new building activity in the mail each month. Derek prepaid an

8

-month subscription for his daughter. He signed up during their holiday sale and received

15

\$

off the total cost. Derek paid

81

\$

\newline

Which equation can Derek use to find

x

, the regular cost per month?

\newline

\newline

8(x - 15) = 81

\newline

15x - 8 = 81

\newline

15(x - 8) = 81

\newline

8x - 15 = 81

Tasty Trunk Treats sends a selection of snacks in the mail each month. Andy bought a

3

-month subscription for a friend. He used a one-time coupon and received

5

\$

off the total cost. Andy paid

37

\$

\newline

Which equation can you use to find the regular cost,

m

, for each month?

\newline

\newline

3(m - 5) = 37

\newline

5m - 3 = 37

\newline

3m - 5 = 37

\newline

5(m - 3) = 37

Ellen is excited to learn how to ski. She went to White Peaks Mountain, rented a pair of skis for

45

\$

4

hours of group skiing lessons. Ellen paid

165

\$

\newline

Which equation can you use to find how much White Peaks charges,

h

, for each hour of group skiing lessons?

\newline

\newline

45(h + 4) = 165

\newline

45h + 4 = 165

\newline

4h + 45 = 165

\newline

4(h + 45) = 165

Katie took a plane to visit her grandparents for the summer. At the airport, she paid to check

3

bags. Since all of her bags were over the weight limit, she had to pay an additional

6\$

fee for each bag. Katie paid a total of

102\$

to check her bags.

\newline

Which equation can you use to find the amount of money,

x

, it costs to check a bag that's under the weight limit?

\newline

\newline

3x + 6 = 102

\newline

3(x + 6) = 102

\newline

6(x + 3) = 102

\newline

6x + 3 = 102

Hearth Knits Clothing Store is having its annual winter sale. Carter buys

4

wool scarves, one for each member of his family. During the sale, wool scarves are selling for

5\$

less than full price. Carter pays a total of

72\$

for the scarves.

\newline

Which equation can Carter use to find

f

, the cost of each wool scarf at full price?

\newline

\newline

4f - 5 = 72

\newline

5(f - 4) = 72

\newline

4(f - 5) = 72

\newline

5f - 4 = 72

Riley and her friends went to the Color Splat paint-tag course last weekend. The course charges

40\$

for an hour of group tag plus a rental fee for each paint marker. Riley's group played for one hour, rented 6 paint markers, and paid a total of

94\$

\newline

Which equation can you use to find the rental fee,

x

, for each paint marker?

\newline

\newline

6x + 40 = 94

\newline

6(x + 40) = 94

\newline

40(x + 6) = 94

\newline

40x + 6 = 94

Cassie prepaid a

6

-month membership to the Summer Lotus yoga studio. She received a one-time discount of

40

\$

for prepaying. Cassie paid a total of

650

\$

\newline

Which equation can Cassie use to find

m

, the regular cost per month?

\newline

\newline

40m - 6 = 650

\newline

40(m - 6) = 650

\newline

6(m - 40) = 650

\newline

6m - 40 = 650

Gwen and her scout troop are heading to the Treetop Glider zip-line course. They plan to purchase the group package, which will be

504

\$

14

6

\$

less per person than the normal cost for an individual.

\newline

Which equation can Gwen use to find

x

, the normal cost of an individual?

\newline

\newline

6x - 14 = 504

\newline

14x - 6 = 504

\newline

14(x - 6) = 504

\newline

6(x - 14) = 504

Vijay is building a new rectangular enclosure in his backyard for his chickens. He has

40

feet of fencing material and he wants the width of the enclosure to be

8

l

is the length of the enclosure, and Vijay uses all of the fencing material, which equation best models the situation?

\newline

1

\newline

l+8=40

\newline

2 l+8=40

\newline

2(l+8)=40

\newline

2 l+2(l+8)=40

Solve the following system of linear equations:

\newline

x_1+x_2+x_3=2

\newline

2x_1-x_2+x_3=9

\newline

2x_1+3x_2+4x_3=4

\newline

Determine the values of

x_1, x_2, x_3

In a restaurant, the daily menu is mounted on wallboard. The printed region with today's entrees includes

216

square inches of text. If there are two-inch margins on the sides and three-inch margins at the bottom and the top, what are the dimensions of the smallest piece of wallboard that can be used for the menu?

\newline

1

\newline

12 \prime \prime \times 20 \prime \prime

\newline

12 \prime \prime \times 24 \prime \prime

\newline

16 \prime \prime \times 20 \prime \prime

\newline

16 \prime \prime \times 24 \prime \prime

\newline

(E) None of these

In a restaurant, the daily menu is mounted on wallboard. The printed region with today's entrees includes

216

square inches of text. If there are two-inch margins on the sides and three-inch margins at the bottom and the top, what are the dimensions of the smallest piece of wallboard that can be used for the menu?

\newline

1

\newline

12 \prime \prime \times 20 \prime \prime

\newline

12 \prime \prime \times 24 \prime \prime

\newline

16 \prime \prime \times 20 \prime \prime

\newline

16 \prime \prime \times 24 \prime \prime

\newline

(E) None of these