In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. if one sweater and four shirts cost $52, while four sweaters and five shirts cost $98. find the price of one sweater and the price of one shirt.

1 Sweater = $12

1 Shirt = $10

1st.

Sw = y

Sh = x

2nd: set the problem into a function.

- One sweater and four shirts cost $52.

y+x+x+x+x = $52

and

- Four sweaters and five shirts cost $98.

y+y+y+y+x+x+x+x+x = $98

3rd.

y+x+x+x+x = $52

y = 52-x-x-x-x

y = 52-4x

4th. if y = 52-4x, we will substitute on the second equation.

y+y+y+y+x+x+x+x+x = $98

52-4x+52-4x+52-4x+52-4x+5x = 98

208-16x+5x = 98

-16x+5x = 98-208

-11x = -110

x = -110/-11

x = 10

5th. if x = 10, now that we know what x equals to, we will substitute on the first equation to find out what y equals to.

y = 52-4x

y = 52-(4)(10)

y = 12

,,,,,,

Sweater = $12

Shirt = $10

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step-by-step explanation: