Answer:
[tex]\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..[/tex]
Step-by-step 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
[tex]\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..[/tex]
Substitute second equation into the first one:
[tex]25x+10(x+5)=400,\\ \\25x+10x+50=400,\\ \\35x=350,\\ \\x=10,\ y=10+5=15.[/tex]
10 quaters and 15 dimes
