Answer:
34 nickels
Step-by-step explanation:
First, consider the value if they were all dimes. That would be 61×$0.10 = $6.10. Next, realize this is more than the actual amount by 1.70. Of course, replacing one of the 61 dimes by a nickel reduces the total amount by $.05, so we must have ...
$1.70/$0.05 = 34
nickels in the mix.
Abby has 34 nickels.
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Alternate solution methods
I like to solve these using number sense, as above. Equivalently, an equation can be written using n to represent the number of nickels. The total value is then ...
.05n + .10(61 -n) = 4.40
-.05n +6.10 = 4.40 . . . . . . eliminate parentheses
-.05n = -1.70 . . . . . . . . . . . subtract 6.10
n = -1.70/-.05 = 34
Hopefully, you notice some similarities between this solution and the one in words, above.
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Often, you will see this sort of problem formulated using two equations.
n + d = 61 . . . . . . . . . . number of coins (d=#of dimes)
.05n +.10d = 4.40 . . . .value of coins
If we solve this by substitution, we can use d=61-n, and get ...
.05n +.10(61-n) = 4.40 . . . . . . looks like our equation in the previous section
