Isabelle has $5.45 in her purse. If she has five more nickels than dimes, and twice as many quarters than dimes, how many of each type of coin does she have?
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> answer is 8 dimes, 13 nickels, and 16 quarters.
⚽ Correct Question ⚽
Isabelle has $5.45 in her purse. If she has five more nickels than dimes, and twice as many quarters than dimes, how many of each type of coin does she have?
⚽ Solution ⚽
- From our problem, we see that she has $5.45 in nickels, dimes, and quarters. We let each type of coin be represented by its first letter. Our first equation is 5N+25Q+10D=545.
Since she has five more nickels than dimes, we have N=5+D.
Since she has twice as many quarters than dimes, we have Q=2D.
- Our next step is to substitute these into our equation for N and Q.
- 5(5+D)+25(2D)+10D=545
We distribute and simplify.
- 25+5D+50D+10D=545
We add like terms.
- 25+65D=545
Lastly we subtract 25 from both sides and divide by 65 to get D=8. This means we have 8 dimes.
Using our equations from above we have N=5+D=5+8=13 and Q=2D=2(8)=16. This means we have 13 nickels and 16 quarters.
Our final answer is 8 dimes, 13 nickels, and 16 quarters.
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