Question 1183070: John went to his favorite Young Men clothing store and bought himself a new shirt, pants and pair of shoes. His pants cost twice as much as his shirt. His shoes cost $50 less than twice the cost of his pants. With 8% sales tax, he paid a total of $324. What was the cost of each of the item?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
s = cost of shirt
p = cost of pants
h = cost of shoes
All costs are in dollars. These costs are before tax and they don't involve anything like coupons, discounts, sales promotions, etc.
"his pants cost twice as much as his shirt" means
p = 2s
His shoes cost $50 less than twice the cost of his pants tells us that
h = 2p-50
Plug in the previous equation we set up to get
h = 2p-50
h = 2(2s)-50
h = 4s-50
This way, we have both p and h in terms of s.
The total cost of everything, before tax, is:
T = s+p+h
T = s+2s+4s-50
T = 7s-50
Again, this is before tax.
With the 8% tax considered, we multiply that value of T by 1.08
So 1.08*(7s-50) represents the final cost after tax is considered.
Set this equal to 324 and solve for s
1.08*(7s-50) = 324
7s-50 = 324/1.08
7s-50 = 300
7s = 300+50
7s = 350
s = 350/7
s = 50
The shirt costs $50
Use this to find the value of p
p = 2s
p = 2*50
p = 100
The pair of pants cost $100
Then use that value of p to find h
h = 2p-50
h = 2*100-50
h = 200-50
h = 150
The pair of shoes cost $150
Or you could compute it like this
h = 4s-50
h = 4*50-50
h = 200-50
h = 150
Either way, we get the same value of h.
Note that the total cost before sales tax is
s+p+h = 50+100+150 = 300
Then we pay 0.08*300 = 24 dollars in sales tax to get a total cost of 300+24 = $324
Or we could say as a shortcut: 1.08*300 = 324
This helps confirm the answers.
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Answers:
Shirt costs $50
Pants cost $100
Shoes cost $150
Answer by greenestamps(13200)  (Show Source):
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