Question

Roberta has $4.00 in dimes and quarters. She has 5 more dimes than quarters. Write a system of equations that you could use to find how many dimes and quarters she has.

Answer 1

`\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..`

Explanation:

Let x be the number of quaters and y be the number of dimes Roberta has.

1. Quater is equal to 25 cents, then x quaters is equal to 25x cents. Dime is equal to 10 cents, then y dimes is equal to 10y cents. $4.00=400 cents, then

25x+10y=400.

2. Roberta has 5 more dimes than quarters, then

y=x+5.

3. The system of equations is

`\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..`

Substitute second equation into the first one:

`25x+10(x+5)=400,\\ \\25x+10x+50=400,\\ \\35x=350,\\ \\x=10,\ y=10+5=15.`

10 quaters and 15 dimes