SOLUTION: Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts costs $15. If she bought a total of 7 shirts then how many of each kind did she buy

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Question 1200103: Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts costs $15. If she bought a total of 7 shirts then how many of each kind did she buy
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39615) (Show Source):
You can put this solution on YOUR website!
7 total shirts
h of the fancy shirts ($28 each)
7-h of the plains shirts ($15 each)

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Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

x = number of fancy shirts
7-x = number of plain shirts

Type Number Cost

Fancy x 28x

Plain 7-x 15(7-x) = 105-15x

Total 7 $131

Total cost:
fancy + plain = $131
28x + (105-15x) = 131
13x + 105 = 131
13x = 131 - 105
13x = 26
x = 26/13
x = 2

Fancy = x = 2
Plain = 7-x = 7-2 = 5

Check:
1 fancy shirt = $28
2 fancy shirts = 2*$28 = $56
1 plain shirt = $15
5 plain shirts = 5*$15 = $75
2 fancy + 5 plain = $56 + $75 = $131 total
2 fancy + 5 plain = 7 shirts total
The answers are confirmed.

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Another approach:

Let's say all 7 shirts were fancy.
7*28 = 196
She would spend $196

The gap from $131 to $196 is
196-131 = 65
Her total cost needs to drop by $65 to get to $131

Each time we subtract 1 fancy shirt, and add a plain shirt, we subtract a net cost of $13 (since -28+15 = -13)
Then notice how 13 is a factor of 65
65 = 13*5
This tells us that we need to introduce 5 plain shirts

The 7 fancy shirts will drop to 7-5 = 2 fancy shirts.

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Another approach:

x = number of fancy shirts
y = number of plain shirts

x+y = 7 ... shirt count equation
28x+15y = 131 .... shirt cost equation

Graph those two equations using something like Desmos or GeoGebra. Both are free.

The two equations intersect at (2,5)
Meaning we have x = 2 fancy shirts and y = 5 plain shirts

x+y = 7 in green
28x+15y = 131 in blue

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Answers:
2 fancy and 5 plain