Question 1066531
<font color=black size=3>n = number of nickels
d = number of dimes


We have 45 coins of nickels and dimes only, so,

n+d = 45
n = 45-d


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The value of the nickels is 5n cents while the value of all the dimes is 10d cents. In total, the value is 5n+10d. This must be set equal to 310 ($3.10 = 310 cents)


So we have this equation
5n+10d = 310


Plug in n = 45-d and solve for d
5n+10d = 310
5(n)+10d = 310
5(45-d)+10d = 310
5(45)+5(-d)+10d = 310
225-5d+10d = 310
225+5d = 310
225+5d-225 = 310-225
5d = 85
5d/5 = 85/5
d = 17


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Use this to find the value n


n = 45-d
n = 45-17
n = 28


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Summary:
n = 28 and d = 17
There are <font color=red>28 nickels and 17 dimes</font></font>