Question

Kris spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. Is kris bought a total of 7 then how many of each kind did she buy?

Answer 1

Number of fancy shirts Kris bought = 2

Number of plain shirts Kris bought = 5

Explanation:

Total number of shirts = 7

Let number of fancy shirts be =
`x`

Let number of plain shirts be =
`y`

Total number of shirts =
`x+y`

So, we have a sum equation as:

`x+y=7`

Total cost of shirts = $131

Cost of a fancy shirt = $28

Cost of
`x` fancy shirts in dollars can be given as =
`28x`

Cost of a plain shirt = $15

Cost of
`y` plain shirts in dollars can be given as =
`15y`

Total cost of shirts =
`28x+15y`

So, we have a cost equation as:

`28x+15y=131`

The system of equations is :

A)
`x+y=7`

B)
`28x+15y=131`

Rearranging equation A, to solve for
`y` in terms of
`x`

Subtracting both sides by
`x`

`x+y-x=7-x`

`y=7-x`

Substituting value of
`y` we got from A into equation B.

`28x+15(7-x)=131`

Using distribution.

`28x+105-15x=131`

Simplifying.

`13x+105=131`

Subtracting both sides by 105.

`13x+105-105=131-105`

`13x=26`

Dividing both sides by 13.

`(13x)/(13)=(26)/(13)`

`x=2`

We can plugin
`x=2` in the rearranged equation A to get value of
`y`

`y=7-2`

∴
`y=5`

So, number of fancy shirts Kris bought = 2

Number of plain shirts bough = 5