Answer:
21 Dimes and 16 Quarters
Step-by-step explanation:
Let D and Q stand for the numbers of Dimes and Quarters, respectively.
We learn that Steve has 37 total coins:
D + Q = 37
We also know that their total value is $6.10. Let's use cents, instead of $ for the rest of the calculation. You can use either, but I like playing with money.
Using cents:
10D + 25Q = 610 [10 pennies times the number of Dimes gives the number of pennies. 25 pennies times each quarter gives us the pennies from all the quarters. Their sum is 610 pennies.]
We have 2 equations and 2 unknowns, so we are able to solve the problem, after we do some substitution.
We can approach this in several ways, but I like the idea of changing the first equation to find the number of Dimes, which will be:
D + Q = 37
D = 37 - Q
Now use this value for D in the second equation:
10D + 25Q = 610
10(37 - Q) + 25Q = 610
370 - 10Q + 25Q = 610
15Q = 610 - 370
15Q = 240
Q = 16 quarters
Since we already derived D = 37 - Q, we can say:
D = 37 - 16
D = 21 Dimes
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Check these results. Are 21 Dimes and 16 Quarters solutions to the scenario?
Does Steve have 37 coins: 21 Dimes and 16 Quarters = 37 Coins. YES
Does Steve have $6.10? 21*($0.10) + 16*($0.25) = $2.10 + $4.00 = $6.10 YES
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