Question

Arianna has a total of 34 nickels and dimes. together the coins total $2.05. how many nickels does arianna have

Answer 1

N = amount of nickels

D = amount of dimes

well, we know she has 34 coins total, so whatever N and D might be, we know that their sum is 34, so N + D = 34.

So all the coins add up to $2.05, which if we put in pennies that's 205 pennies, how many pennies in 1 nickel? well, 5, how many pennies in a dime? well, 10, so the amount of 205 pennies is really 5N + 10D.

`N+D=34\implies D=34-N \\\\[-0.35em] ~\dotfill\\\\ 5N+10D=205\implies \stackrel{\textit{substituting from above}}{5N+10(34-N)=205}\implies 5N+340-10N=205 \\\\\\ -5N+340=205\implies 340=5N+205\implies 135=5N \\\\\\ \cfrac{135}{5}=N\implies \boxed{27=N}`