Answer:
Brandon has 18 Dimes and 33 Quarters [Beware: The problem does not state that Brandon owns the coins - he just has them. Check your pockets]
Step-by-step explanation:
Let D and Q stand for the numbers of Dimes(D) and Quarters(Q). I'll use pennies instead of dollars, so avoid the clutter of decimal points.
We are told that:
Q = 2D - 3 [The number of quarters is 3 less than twice the number of dimes.]
and
25Q + 10D = 1005 [total value of $10.05]
Substitute the value of Q in the first equation in the second, so that we have an equation with just one unknown, D.
25(2D-3) + 10D = 1005
50D - 75 + 10D = 1005
60D = 1080
D = 18
Q = 2D - 3
Q = 2(18) - 3
Q = 33
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Check
25Q + 10D = 1005
25(33) + 10(18) = 1005 ?
825 + 180 = 1005 YES
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Q = 2D - 3 ?
33 = 2(18) - 3 YES
