Answer:
Lily has 7 Quarters and 10 Dimes
Step-by-step explanation:
Let's use pennies instead of $.
Let <u>D</u> and <u>Q</u> stand for the numbers of Dimes and Quarters, respectively.
We are told that there are 17 coins total:
<u> D + Q = 17</u>
We also learn that they amount to 275 (pennies). We can write that as:
<u>10D + 25Q = 275</u> [Each D is worth 10 pennies, etc.]
We have two equations and two unknowns. We can rearrange one equation to find the value of either of the unknowns, and then use that it the second equation.
I'll rearrange the first:
D + Q = 17
<u> D = 17 - Q</u>
Now use this value of D in the second equation:
10D + 25Q = 275
10(17-Q) + 25Q = 275
170 - 10Q + 25 Q = 275
15Q = 105
<u>Q = 7 : 7 Quarters.</u>
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Since D + Q = 17:
D + 7 = 17
<u>D = 10 Dimes</u>
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Let's check these results:
Q = 7 Quarters
D = 10 Dimes
1. Is this 17 coins in total? (7+10 = 17) <u>YES</u>
2. Does this add to $2.75? (10*10) + (7*25) = 275 cents?
(100 + 176) = 275 (cents) <u>YES</u>
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Lily has 7 Quarters and 10 Dimes
