Question

1. I've posted this question before (once, the other post wasn't me)and I have still got no help.


Peg spends $7.50 a week for grapefruit. When grapefruit are out of season, she gets 1 fewer grapefruit than when they are in season. If the price decreases by $3 per dozen in season, how many dollars will it cost to buy a dozen grapefruit out of season?

Answer 1

Let the price per dozen in season be $x
let the price per dozen out of season be $(x+3)

So in season for $7.50 she can buy 7.5/x dozen
or 90/x grapefruits

Out of season for $7.50 she can buy 7.5/(x+3) dozen or 90/(x+3) grapefruits

so 90/x - 90/(x+3) = 1

multiply by x(x+3)
90(x+3) - 90x = x(x+3)
expand and simplify
x^2 + 3x - 270 = 0
(x+18)(x-15) = 0
x = -18 or x = 15 , but clearly x > 0

price out of season was defined as x+3
so out of season they sold at $18 per dozen, WOW!

check:
in season she could buy 7.5/15 = .5 dozen or 6 grapefruits
out of season she could buy 7.5/18 or .4166667 dozen or 5 grapefruits

is 6-5 = 1 ? YES