ANSWER:
60 nickels
15 dimes
STEP-BY-STEP 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.
[tex]0.05\cdot4x+0.10\cdot x=4.5[/tex]Now we solve for x to find the number of dimes, like this:
[tex]\begin{gathered} 0.2x+0.1x=4.5 \\ 0.3x=4.5 \\ x=\frac{4.5}{0.3} \\ x=15 \\ \text{ and for nickels:} \\ 4x=4\cdot15=60 \end{gathered}[/tex]Which means that Gloria has 60 nickels and 15 dimes
