Question

Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 5 sweaters for $99 or she is able to buy 6 shirts and 4 sweaters for $90. How much does a shirt cost? How much does a sweater cost?

Answer 1

Given :

The cost of 3 shirts and 5 sweaters is $99 .

The cost of 6 shirts and 4 sweaters is $90.

To determine :

The sweater cost and shirt cost each.

Explanation :

Let the shirt cost be x.

Let the sweater cost be y.

Then the equation formed is

`3x+5y=99\ldots\ldots\ldots\ldots\ldots\ldots..1`
`6x+4y=90\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots2`

Solve the equation 1 and 2 to find x and y with the help of elimination method.

Multiply by 2 in equation 1.

`6x+10y=198\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.\ldots3`

Solve equation 2 and 3 by subtraction,

`(6x+10y-198)-(6x+4y-90)=0`
`6y-198+90=0`
`6y=108`
`y=18`

The value of y is 18 and now substitute the value of y in equation 2 to find x.

`6x+4y=90`
`6x+4*18=90`
`6x=90-72`
`6x=18\Rightarrow x=3`

The value of x is 3.

Answer :

The cost of shirt is 3 dollar .

The cost of sweater is 18 dollar.