word problem.. t-shirts...?

Question

rima bought a case of concert t-shirts for $450.00 . she kept two t-shirts for herself and solf the rest for $560, making a profits of $10 on each t-shirts. how many t-shirts were in the case?

please explain thx in advance.. =D

Answer 1

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Let t be the number of t-shirts bought.

Let c be the cost of one t-shirt.

Let t-2 be the number of t-shirts sold.

Let c+10 be the sale price of one t-shirt

Rima bought t shirts at a cost of c each for a total of $450.

tc = 450

Then she sold (t - 2) shirts at a price of (c+10) for a total of $560.

(t - 2)(c + 10) = 560

That's two equations and two unknowns which can easily be solved.

Solve the first equation for one variable:

c = 450/t

Plug this into the second equation:

(t - 2)(450/t + 10) = 560

Multiply both sides by t:

(t - 2)(450 + 10t) = 560t

Expand out on the left using FOIL:

450t + 10t² - 900 - 20t = 560t

Group like terms on the left:

10t² + 450t - 20t - 560t - 900 = 0

10t² - 130t - 900 = 0

Divide both sides by 10 to simplify things:

t² - 13t - 90 = 0

Factor that:

(t - 18)(t + 5) = 0

That means Rima either bought 18 shirts or -5 shirts. Only one answer makes sense.

Double-check the answer:

18 shirts x $25 = $450 (bought)

16 shirts x $35 = $560 (sold)

Answer:

18 shirts

P.S. She made a profit of $10 for each shirt sold. That's 16 x $10 = $160. But she kept 2 shirts for herself worth $50. That's why the difference is $110.

Answer 2

the difference between the purchase price and the selling price its the profit 560 -450 = 110

the profit is 10 x the number of shirts remaining

or the original number less the 2 she took

n-2

560- 450= 10(n-2)

110 = 10n-20

10n= 130

n=13

13 shirts in the case