algebra and fractions

Question

In a chest there are some gold coins. Captain takes half the coins. Sally takes a fourth of the coins. There are three coins left. How many coins were there in the chest at the start.

Answer 1

There are total x coins.

Captain (c) takes (1/2)x coins

Sally (s) takes (1/4)x coins

There are 3 coins left.

This means that the total amount of coins are:

(1/2)x + (1/4)x + 3

so, you must solve for x by using this formula:

(1/2)x + (1/4)x + 3 = x

Change all x fractions to a common denominator:

(2/4)x + (1/4)x + 3 = (4/4)x

Solve for x:

(1/4)x + 3 = (2/4)x

3 = (1/4)x

Multiply by 4 to get rid of the denominator:

12 = x

You can now check this by substitution 12 for x.

(1/2)12 + (1/4)12 + 3

= 6 + 3 + 3

= 12

This has been checked and is correct