Answer:
Lily has 10 dimes and 7 quarters
Step-by-step explanation:
Let x be the number of dimes and y be the number of quarters Lily has in her pocket.
If there are 17 coins in all, then
[tex]x+y=17[/tex]
The amount in dimes is 10x cents, the amount in quarters is 25y cents. Lily has $2.75 = 275 cents in her pocket, then
[tex]10x+25y=275[/tex]
From the first equation,
[tex]x=17-y[/tex]
Substitute it into the second equation:
[tex]10(17-y)+25y=275\\ \\170-10y+25y=275\\ \\25y-10y=275-170\\ \\15y=105\\ \\y=7\\ \\x=17-y=17-7=10[/tex]
Lily has 10 dimes and 7 quarters
