Question

Lily has $2.75 in her pocket, consisting of dimes and quarters. If there are 17 coins in all, how many of each does she have?

Answer 1

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

$x+y=17$

The amount in dimes is 10x cents, the amount in quarters is 25y cents. Lily has $2.75 = 275 cents in her pocket, then

$10x+25y=275$

From the first equation,

$x=17-y$

Substitute it into the second equation:

$10(17-y)+25y=275\\ \\170-10y+25y=275\\ \\25y-10y=275-170\\ \\15y=105\\ \\y=7\\ \\x=17-y=17-7=10$

Lily has 10 dimes and 7 quarters