Question

Gloria has $ 4.50 worth of change in nickels and dimes. If she has 4 times as many nickels as dimes, how many of each type of coin does she have?

Answer 1

60 nickels

15 dimes

Explanation:

We can determine the number of coins of each type by establishing the following system of equations with the help of the statement:

Let x be the number of dimes and let 4x be the number of nickels.

`0.05\cdot4x+0.10\cdot x=4.5`

Now we solve for x to find the number of dimes, like this:

`\begin{gathered} 0.2x+0.1x=4.5 \\ 0.3x=4.5 \\ x=(4.5)/(0.3) \\ x=15 \\ \text{ and for nickels:} \\ 4x=4\cdot15=60 \end{gathered}`

Which means that Gloria has 60 nickels and 15 dimes