Question

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. She bought seven total shirts. How many fancy and fancy and plain shirts did Kristin buy?

Answer 1

The number of plain shirts bought is 5 and number of fancy shirts bought is 2

Solution:

Let number of plain shirts bought be "a"

Let number of fancy shirts bought be "b"

Given that Kristin bought seven total shirts

plain shirts bought + fancy shirts bought = 7

a + b = 7 ----- eqn 1

Also that Kristin spent $131 on shirts and Fancy shirts cost $28 and plain shirts cost $15

15a + 28b = 131   ---- eqn 2

Multiply first equation by 28 to eliminate b:

28a + 28b = 196  ---- eqn 3

subtracting eqn 2 from eqn 3

28a + 28b = 196

15a + 28b = 131

(-) ------------------

13a = 65

a = 5

Substitute a = 5 in eqn 2

15(5) + 28b = 131

75 + 28b = 131

28b = 56

b = 2

Thus the number of plain shirts bought is 5 and number of fancy shirts bought is 2

Answer 2

Kristin bought 2 fancy shirts and 5 plain shirts.

Step-by-step explanation:

Amount spent on shirts = $131

Cost of one fancy shirt = $28

Cost of one plain shirt = $15

Shirts bought = 7

Let,

x be the number of fancy shirts bought

y be the number of plain shirts bought

According to given statement;

x+y=7    Eqn 1

28x+15y=131    Eqn 2

From Eqn 1

$x=7-y$

Putting this value of x in Eqn 2

$28(7-y)+15y=131\\196-28y+15y=131\\-13y=131-196\\-13y=-65$

Dividing both sides by -13

$\frac{-13y}{-13}=\frac{-65}{-13}\\y=5$

Putting y=5 in Eqn 1

$x+5=7\\x=7-5\\x=2$

Kristin bought 2 fancy shirts and 5 plain shirts.

Keywords: linear equation, substitution method

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