Question

Billy had a sum of money. He bought 12 identical pencils using 3/5 of the money. When he was given another $0.80, he used it with the remaining money to buy another 10 more similar pencils. How much money did Billy have at first?

Answer 1

Amount Billy had at start ---- x
he spent (3/5)x on 12 pencils
so cost per pencil = (3x/5) ÷ 12 = 12(5/(3x)) = x/20

amount he has left after buying the 12 pencils = (2/5)x = 2x/5
gets 0.80 more, so now he has

2x/5 + .8

number of pencils he now buys = 10
cost of those 10 pencils = 10(x/20) = x/2

x/2 = 2x/5 + .8
multiply each term by 10, to clear fractions
5x = 4x + 8
x = 8

<b>So he had $8.00 at the start</b>

check:
he spent 3/5 of 8.00 or 4.80 on 12 pencils
so cost per pencil = 4.80/12 = 0.40

Money left = 3.20 plus the extra .80 to get 4.00
at 40 cents a pencil he can buy 10 more

My answer if correct