Question

Dave has a collection of 47 coins. Some are $10 coins and the rest are $20 coins. If the face value is $710, how many of each denomination does he have?

Answer 1

Answer: he had twenty three $10 coins and twenty four $20 coins.

Explanation:

Let x represent the number of $10 coins that he has.

Let y represent the number of $20 coins that he has.

Dave has a collection of 47 coins. This means that

x + y = 47

Some are $10 coins and the rest are $20 coins. If the face value is $710, it means that

10x + 20y = 710- - - - - - - - - -1

Substituting x = 47 - y into equation 1, it becomes

10(47 - y) + 20y = 710

470 - 10y + 20y = 710

- 10y + 20y = 710 - 470

10y = 240

y = 240/10

y = 24

x = 47 - y = 47 - 24

x = 23