Question

Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has.

Answer 1

• 0.25q +0.10d = 4.20
• q = 2d

Explanation:

Let q represent the number of quarters, and d represent the number of dimes.

0.25q +0.10d = 4.20 . . . . . the value of the coins

q = 2d . . . . . . . . . . . . . . . the relation between the numbers of coins.

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Additional comment

Using substitution, the equation simplifies to ...

0.60d = 4.20

d = 7

q = 14

Note that the coins can be grouped into groups of 2 quarters and 1 dime. The value of the group is $0.60, and the number of dimes is equal to the number of groups. Thinking about the problem in this way gets you immediately to the single equation 0.60d = 4.20.