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?
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
How would you check it?
If c = .2
n = 6/.2 = 30
so sold 25 for .3 so got 25*.3 = 7.5 sure enough
thank you!
You are welcome :)
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.
To solve this problem, we can break it down into smaller steps and use algebra to find the cost of a box of candy.
Step 1: Let's start by figuring out the number of boxes the confectioner bought. We know that he purchased several boxes of candy for $6, but we don't have the exact quantity. So, let's assume the confectioner bought x boxes.
Step 2: The confectioner gave five boxes to his children, so he is left with x - 5 boxes to sell.
Step 3: The confectioner sold the remaining boxes at 10 cents more per box than he paid for them. This means the selling price per box is $0.10 more than the cost per box. So, the selling price is $x + $0.10.
Step 4: We now need to calculate the confectioner's profit. We know that the profit made on the original cost is 25%, which means the profit is 25% of $6. Therefore, the profit is 0.25 * $6 = $1.50.
Step 5: The profit is calculated as the selling price minus the original cost. So, we can set up the equation: Selling Price - Original Cost = Profit.
Substitute the values: ($x + $0.10) - $6 = $1.50.
Step 6: Now, let's solve the equation for x to find the number of boxes purchased:
$x + $0.10 - $6 = $1.50.
Simplify: $x - $5.90 = $1.50.
Move the constant term to the other side: $x = $5.90 + $1.50.
Simplify: $x = $7.40.
Step 7: We have the number of boxes purchased, x = $7.40. Now, we need to find the cost of a box of candy. To do this, we divide the total cost by the number of boxes: $6 / $7.40.
Therefore, a box of candy cost the confectioner $0.81 (rounded to the nearest cent).