How can I solve this?

Question

Maggie and Mia go shopping together. At the fashion Bee, all shirts cost one price and all sweaters cost one price. Maggie buys 2 shirts and 2 sweaters for $86. Mia buys 3 shirts and 1 sweater for $81. What is the cost of a shirt and a sweater?

Answer 1

You can use a system of equations

let x be shirts and y be sweaters.

Maggie bought

2x + 2y = 86

Mia bought

3x + y = 81

Multiply Mia's purchase by -2 and add that to Maggie's purchase to eliminate y

-6x - 2y = -162

2x + 2y = 86

-4x = -76

Divide both sides by -4

x = 19

Substitute 19 for x in Maggie's purchase to find y

2(19) + 2y = 86

38 + 2y = 86

Subtract 38 for both sides

2y = 48

Divide both sides by 2

y = 24

Check both x and y in Mia's original purchase

3x + y = 81

3(19) + 24 = 81

57 + 24 = 81

Shirts cost $19 each

Sweaters cost $24 each

I hope this helps please send me a message if you have any questions.

Answer 2

Let x be the price of a shirt and y be the price of a sweater

Then we can set up a system of equations using the given information:

2x+2y=86

and

3x+y=81

Solve the second equation for y and substitute it into the first equation

3x+y=81

y=81-3x

2x+2y=86

2x+2(81-3x)=86

2x+162-6x=86

-4x+162=86

-4x=-76

x=19 is the price of a shirt

Plug x into 3x+y=81and solve for y

3(19)+y=81

57+y=81

y=24 is the price of a sweater