word problem.. t-shirts...?
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
- PuzzlingLv 71 decade agoFavorite Answer
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
(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)
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.
- Stephen YLv 61 decade ago
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
560- 450= 10(n-2)
110 = 10n-20
13 shirts in the case