Question

A confectioner perchased several boxes of candy for $6. He gave five boxes to his children, and sold the rest at 10 cents more per box than he had paid for them, and made a profit of 25% on his original cost. How much did a box of candy cost him?

Answer 1

1.25 * 6 = 7.5
profit = 1.5

let cost per box = c
sales price = s = c+.1
bought n
gave away 5
sold (n-5)

cost = n c = 6 so n=6/c
sales = (n-5)(c+.1)
so
(n-5)(c+.1) - 6 = 1.5

(6/c -5)(c+.1) = 7.5

6 -5c + .6/c -.5 = 7.5

-5c + .6/c = 2
-5 c^2 -2 c + .6 = 0

5 c^2 + 2 c -.6 = 0

c = [ -2 +/- sqrt(4 + 12) ]/10

c = [-2 + 4 ]/10

c = 0.2 or 20 cents

Answer 2

How would you check it?

Answer 3

If c = .2
n = 6/.2 = 30
so sold 25 for .3 so got 25*.3 = 7.5 sure enough

Answer 4

thank you!

Answer 5

You are welcome :)

Answer 6

Bought X boxes.
Sold (x-5) boxes.

Cost = $Y per box
Selling price = $(y+0.1) per box.

P = $6 * 1.25 = 7.50 = Sale price.

(x-5)(y+0.1) = 7.50
xy + 0.1x - 5y - 0.5 = 7.5

Eq1: xy + 0.1x - 5y = 8

Eq2: xy = $6.00
Y = 6/x
In Eq1, replace Y with 6/x:
6 + 0.1x - 30/x = 8
0.1x - 30/x = 2
Multiply both sides by X:
0.1x^2 - 30 = 2x
0.1x^2 - 2x - 30 = 0
Multiply both sides by 10:
x^2 - 20x - 300 = 0
(x+10)(x-30) = 0

x+10 = 0, X = -10.
x-30 = 0, X = 30 Boxes bought.

x-5 = 30 - 5 = 25 Boxes sold.

30 * y = $6.00
Y = $0.20 per box. = Cost.