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You only need to solve for the number of either nickels or dimes. You can subtract that number from 86 to find the other. Since dimes are worth more, let's solve for dimes; we'll use the variable "d". First, make a chart of what we know:
# dimes = "d"; 0.10 each; total cents in dimes = 10d
# nickels = 86 - d, 0.05 each; total cents in nickels = 5(86-d)
Total number/value of coins: total number is 86; total value $6.90, or 690 cents
Now set up the equation:
10d + 5(86-d) = 690
10d + (5 . 86) + (5 . - d) = 690
10d + 430 - 5d = 690
5d + 430 = 690
5d + 430 - 430 = 690 - 430
5d = 260
(1/5)5d = 260 (1/5)
d = 52
If there are 52 dimes, there must be 34 nickels (86 - 52 = 34).
Let's check our work:
52 dimes = $5.20
34 nickels = $1.70
$5.20 + 1.70 = $6.90
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