Question

Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $107, or she is able to buy 2 shirts and 4 sweaters for $154. How many dollars does a shirt cost? How many dollars does a sweater cost?

Answer 1

Let the cost of shirt be x and sweater be y

So,

`\sf2x + 3y = 107 \: - - - (1) \\ \: \sf4x + 2y = 154 - - - (2)`

Solve the equations by elimination method:

For that we would multiply the first equation by 2 and second equation by 1

`\sf4x + 6y = 214 \\ \sf + 4x + 2y = + 154`

Change the signs of bottom equation to eliminate the variable x:

`\sf \cancel{4x} + 6y = 214 \\ \sf \cancel{ - 4x} - 2y = - 154`

`\sf \: 4y = 60 \\ \boxed{ \tt \therefore \: y = 15}`

Thus the cost of one sweater is $15

Now put this value of y in equation 1 to find x:

`4x + 6y = 214 \\ 4x + 6 * 15 = 214 \\ 4x + 90 = 214 \\ 4x = 214 - 90 \\ 4x = 124 \\ x = 31`

Hence, The cost of 1 sweater is $15 and cost of one shirt is $31...