Answer:
Explanation:
Each group of 1 dime and 2 quarters has a value of $0.60. Thus there must be ...
$7.20/$0.60 = 12
groups of coins. That is, there must be 12 dimes and 24 quarters.
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Comment on the problem statement
The problem is over-specified. Any one of the numbers could be left out and you could still determine the number of quarters and dimes.
- Knowing only 36 coins and a 2:1 ratio tells you 12 dimes and 24 quarters.
- Knowing only 36 coins and a value of $7.20 tells you 12 dimes and 24 quarters.
- Knowing only a 2:1 ratio and a value of $7.20 tells you 12 dimes and 24 quarters. (This is the problem we solved above.)
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You may be expected to solve this using an equation or system of equations.
Let d and q represent the numbers of dimes and quarters, respectively. The problem statement gives rise to three equations relating these two variables.
- d + q = 36 . . . . the total number of coins is 36
- q/2 = d . . . . . . . there are half as many dimes as quarters
- 0.10d + 0.25q = 7.20 . . . . . the value of the coins is $7.20
You can solve the system by choosing any two of these equations. For example, using the first two, we can substitute for d to get ...
q/2 + q = 36
3q = 72 . . . . . . . multiply by 2 to eliminate fractions
72/3 = q = 24 . . . . divide by 3
d = 24/2 = 12 . . . . find d from the second equation