Question

4) Tara has $5.50 in dimes and quarters. She has 8

more quarters than dimes. Write and solve a
system of equations to determine how many dimes
Tara has.
X = quarters
y = dimes

Answer 1

Q = amount of quarters

D = amount of dimes

so we know that a quarter is just 25cents, so if we had Q quarters, that's a total of 25*Q or 25Q cents total.

likewise, a dime is 10cents so if we had D dimes that's 10*D or 10D cents.

no matter whatever 10D and 25Q are, we know their sum is $5.50 or 550 cents, 10D + 25Q = 550.

Since Tara has more Q than D, actually she has 8 more, so whatever D is, we know that Q = D + 8.

`\begin{cases} 10D+25Q=550\\\\ Q=D+8 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{10D~~ + ~~25(D+8)~~ = ~~550}\implies 10D+25D+200=550 \\\\\\ 35D+200=550\implies 35D=350\implies D=\cfrac{350}{35}\implies \boxed{D=10} \\\\\\ \stackrel{\textit{since we know that}}{Q=D+8}\implies \boxed{Q=18}`