Question

Amy has four more 20c coins than 5c coins. The total value of all her 20c and 5c is $3.80. How many 5c coins does Amy have?

Answer 1

Amy has 12 5¢ coins

Explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

`x=y+4`

And the total value of all her coins is $3.80. Thus:

`0.2x+0.05y=3.8`

This yields a system of equations:

`\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}`

We can solve by substitution. Substitute the first equation into the first:

`\displaystyle 0.2(y+4)+0.05y=3.8`

Distribute:

`\displaystyle 0.2y+0.8+0.05y=3.8`

Combine like terms:

`\displaystyle 0.25y = 3`

And divide both sides by 0.25. Hence:

`y=12`

Thus, Amy has 12 5¢ coins.

Using the first equation:

`x=y+4`

Substitute:

`x=(12)+4=16`

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.