Question

Aisha owns an apparel store. She bought some shirts and jeans from a wholesaler for $3,900. Each shirt cost $12 and each pair of jeans cost $28. If she sold the shirts at 70% profit and jeans at 125% profit, her total profit was $3,885. How many shirts and jeans did she buy from the wholesalers?

Answer 1

Let the number of shirts be x, and the jeans be y.

Total cost of shirts = 12x
Total cost of Jeans = 28y

This means that: 12x + 28y = 3900..........(a)

Selling price for Shirts 70% profit, means = 100% + 70% = 170% of the cost price

170/100 * 12x = 1.7*12x = 20.4x

Selling price for Jeans 125% profit, means = 100% + 125% = 225% of the cost price

225/100 * 28y = 2.25*28y = 63y

Total profit = 3885, remember total cost = 3900

Total selling price = 3885 + 3900 = 7785

20.4x + 63y = 7785..........(b)


12x + 28y = 3900.............(a)

20.4x + 63y = 7785...........(b)

Solving the simultaneous equation with a programmable calculator:

x = 150, y = 75

150 shirts and 75 jeans.

Answer 2

Let

x-------> the number of shirts

y------> the number of jeans

we know that

`12x+28y=3,900` -------> equation
`1`

If she sold the shirts at
`70\%` profit and jeans at
`125\%` profit, her total profit was
`\$3,885`

so

`1.7*(12x)+2.25*(28y)=3,900+3,885`

`20.4x+63y=7,785` -------> equation
`2`

we have the following system of equations

`12x+28y=3,900` -------> equation
`1`

`20.4x+63y=7,785` -------> equation
`2`

using a graph tool

see the attached figure

The solution of the system is the intersection both graphs

the solution is the point
`(150,75)`

that means

`x=150\ shirts\\y=75\ jeans`

therefore

the answer is

the number of shirts is
`150`

the number of jeans is
`75`