Question

You have 31 coins consisting of nickels and

dimes. The coins total $2.25. How many coins
are nickels? How many are dimes?

Answer 1

There are 14 dimes and 17 nickels.

Explanation:

Let x be number of nickels and let y be number of dimes.

Given that the total is $2.25 and there are 31 coins, we know that:

`0.05x +0.10y = 2.25`

`x+y = 31`

Solving for x yields:

`x=31-y`

We then proceed by plugging that back into the previous equation:

`0.05(31-y)+0.10y=2.25`

`1.55 - 0.05y +0.10y = 2.25\\` --> Distribute

`1.55 +0.05y=2.25` --> add y's together

`0.05y=0.7` --> subtract 1.55

`y=14` --> divide by 0.05

Therefore, x must equal 17, which means you have 14 dimes and 17 nickels.