SOLUTION: Jane purchased a skirt, sweater and a pair of shoes for $138. The sweater is 9/8 of the cost of the skirt. The shoes cost $13 more than the skirt? How much is the cost per item?

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Question 1014305: Jane purchased a skirt, sweater and a pair of shoes for $138. The sweater is 9/8 of the cost of the skirt. The shoes cost $13 more than the skirt? How much is the cost per item?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
a = cost of the skirt.
b = cost of the sweater.
c = cost of the shoes.

a + b + c = 138.

cost of the sweater is 9/8 times the costs of the skirt.

the equation for that is b = 9a/8.

the shoes cost 13 dollars more than the skirt.

the equation for that is c = a + 13

you have 3 equations to work with.

a + b + c = 138
b = 9a/8
c = a + 13

in the equation of a + b + c = 138, replace b with 9a/8 and replace c with a + 13 to get:

a + b + c = 138 becomes a + 9a/8 + a + 13 = 138

combine like terms to get 2a + 9a/8 + 13 = 138.

since 2a = 16a/8, the equation becomes 16a/8 + 9a/8 + 13 = 138

combine like terms again to get 25a/8 + 13 = 138.

subtract 13 from both sides of this equation to get 25a/8 = 138 - 13.

simplify to get 25a/8 = 125.

multiply both sides of this equation by 8 and divide both sides of this equation by 25 to get a = 8*125/25

this results in a = 40

when a = 40:

9a/8 = 9*40/8 = 9*5 = 45.

a + 13 = 40 + 13 = 53.

a = 40
b = 45
c = 53

a + b + c = 40 + 45 + 53 = 138.
this checks out ok.

b = 9a/8 = 9*40/8 = 45.
this checks out ok.

c = a = 13 = 40 + 13 = 53.
this checks out ok.

the cost per item is:

skirt = 40
sweater = 45
shoes = 53.

that's your solution.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
Jane purchased a skirt, sweater and a pair of shoes for $138. The sweater is 9/8 of the cost of the skirt. The shoes cost $13 more than the skirt? How much is the cost per item?

Let price of the skirt be S
Then cost of sweater is: , or
Cost of shoes: S + 13
We then get:

16S + 9S = 1,000 ------- Multiplying by LCD, 8
25S = 1,000
S, or cost of skirt = =
Cost of sweater: =
Cost of shoes: 40 + 13 =