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Math Problems
Algebra 2
Solve a system of equations using any method: word problems
A fruit stand has to decide what to charge for their produce. They need
$
10
\$ 10
$10
for
4
4
4
apples and
4
4
4
oranges. They also need
$
12
\$ 12
$12
for
6
6
6
apples and
6
6
6
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
A Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.50
\$ 1.50
$1.50
for an orange.
\newline
B Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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Ben is \(4\) times as old as Ishaan. \(6\) years ago, Ben was \(6\) times as old as Ishaan.
\newline
How old is Ben now?
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Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher.
\newline
How old is Christopher?
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Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.
\newline
How old is Ben?
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Ben is \(3\) times as old as Daniel and is also \(4\) years older than Daniel.
\newline
How old is Daniel?
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Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.
\newline
How old is Ben now?
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Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.
\newline
How old is Brandon?
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Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.
\newline
How old is Kevin now?
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Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher.
\newline
How old is Ishaan?
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In \(56\) years, Daniel will be \(5\) times as old as he is right now.
\newline
How old is he right now?
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Ben is \(30\) years old and Daniel is \(2\) years old.
\newline
How many years will it take until Ben is only \(3\) times as old as Daniel?
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Ben is \(39\) years old and Ishaan is \(3\) years old.
\newline
How many years will it take until Ben is only \(4\) times as old as Ishaan?
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Kevin is \(39\) years old and Daniel is \(3\) years old.
\newline
How many years will it take until Kevin is only \(4\) times as old as Daniel?
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In \(36\) years, Ishaan will be \(3\) times as old as he is right now.
\newline
How old is he right now?
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Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.
\newline
How old is Ishaan now?
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Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.
\newline
How old is Daniel now?
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Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.
\newline
How old is Brandon now?
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Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.
\newline
How old is Ishaan?
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Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.
\newline
How old is Michael now?
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Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel.
\newline
How old is Daniel?
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A fruit stand has to decide what to charge for their produce. They decide to charge
$
5.30
\$ 5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also plan to charge
$
14
\$ 14
$14
for
2
2
2
apples and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.00
\$ 3.00
$3.00
for an apple and
$
2.30
\$ 2.30
$2.30
for an orange.
\newline
B Yes; they should charge
$
3.00
\$ 3.00
$3.00
for an apple and
$
4.00
\$ 4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
Get tutor help
A fruit stand has to decide what to charge for their produce. They need
$
5.30
\$ 5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also need
$
7.30
\$ 7.30
$7.30
for
1
1
1
apple and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.30
\$ 3.30
$3.30
for an apple and
$
2.00
\$ 2.00
$2.00
for an orange.
\newline
B Yes; they should charge
$
2.00
\$ 2.00
$2.00
for an apple and
$
3.30
\$ 3.30
$3.30
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
Get tutor help
Christopher is \(20\) years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was \(3\) times as old as Christopher.
\newline
How old is Ishaan now?
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Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.
\newline
How old is Michael now?
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Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.
\newline
How old is Christopher now?
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A fruit stand has to decide what to charge for their produce. They need
$
5
\$ 5
$5
for
1
1
1
apple and
1
1
1
orange. They also need
$
15
\$ 15
$15
for
3
3
3
apples and
3
3
3
oranges. Put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
A Yes; they should charge
$
2.00
\$ 2.00
$2.00
for an apple and
$
3.00
\$ 3.00
$3.00
for an orange.
\newline
B Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
4.00
\$ 4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
D
N
o
\mathrm{No}
No
; the system has no solution.
Get tutor help
Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.
\newline
How old is Brandon now?
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In \(16\) years, Ben will be \(3\) times as old as he is right now.
\newline
How old is he right now?
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Ben is \(4\) times as old as Ishaan. \(6\) years ago, Ben was \(6\) times as old as Ishaan.
\newline
How old is Ishaan now?
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Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.
\newline
How old is Kevin now?
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At Imelda's fruit stand, you bought
5
5
5
apples and
4
4
4
oranges for
$
10
\$ 10
$10
, and your friend bought
5
5
5
apples and
5
5
5
oranges for
$
11
\$ 11
$11
.
\newline
Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.25
\$ 1.25
$1.25
for an orange.
\newline
B Yes; they should charge
$
1.20
\$ 1.20
$1.20
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
Get tutor help
Ben is \(12\) years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was \(4\) times as old as Ishaan.
\newline
How old is Ben now?
Get tutor help
A fruit stand has to decide what to charge for their produce. They need
$
10
\$ 10
$10
for
4
4
4
apples and
4
4
4
oranges. They also need
$
15
\$ 15
$15
for
6
6
6
apples and
6
6
6
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.50
\$ 1.50
$1.50
for an orange.
\newline
B Yes; they should charge
$
1.50
\$ 1.50
$1.50
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
Get tutor help
Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.
\newline
How old is Kevin now?
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Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.
\newline
How old is Gabriela now?
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Ben is \(3\) times as old as Daniel and is also \(4\) years older than Daniel.
\newline
How old is Ben?
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Ishaan is \(72\) years old and William is \(4\) years old.
\newline
How many years will it take until Ishaan is only \(5\) times as old as William?
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Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.
\newline
How old is Daniel now?
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Ben is \(12\) years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was \(4\) times as old as Ishaan.
\newline
How old is Ishaan now?
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Tiffany is \(34\) years old and Vanessa is \(6\) years old.
\newline
How many years will it take until Tiffany is only \(3\) times as old as Vanessa?
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Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.
\newline
How old is Daniel now?
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Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel.
\newline
How old is Kevin?
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Christopher is \(20\) years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was \(3\) times as old as Christopher.
\newline
How old is Christopher now?
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases
3
3
3
hot dog meals and
3
3
3
hamburger meals, paying a total of
$
36
\$36
$36
. Mr. Hogan buys
1
1
1
hot dog meal and
3
3
3
hamburger meals, spending
$
26
\$26
$26
in all. How much do the meals cost?
\newline
Hot dog meals cost
$
\$
$
_______ each, and hamburger meals cost
$
\$
$
________ each.
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