Zoe has a total of 16 coins. Some of her coins are dimes and some are nickels. The combined value of her nickels and dimes is $1.35. How many nickels and dimes does she have?

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Answer 1 · 2016-11-26T14:38:24

Zoe has 5 nickles and 11 dimes.

First, let's give what we are trying to solve for names. Let's call the number of nickles $n$ and the number of dimes $d$ .

From the problem we know:

$n + d = 16$ She has 16 coins made up of some dimes and some nickles.

$0.05n + 0.1d = 1.35$ The value of the dimes with the value of the nickles is $1.35.

Next, we solve the first equation for $d$

$n + d - n = 16 - n$

$d = 16 - n$

Next, we substitute $16 - n$ for $d$ in the second equation and solve for $n$ :

$0.05n + 0.1(16 - n) = 1.35$

$0.05n + 0.1*16 - 0.1n = 1.35$

$(0.05 - 0.1)n + 1.6 = 1.35$

$-0.05n + 1.6 = 1.36$

$-0.05n + 1.6 - 1.6 = 1.35 - 1.6$

$-0.05n = -0.25$

$(-0.05n)/(-0.05) = (-0.25)/(-0.05)$

$n = 5$

Now we can substitute $5$ for $n$ in the solution for the first equation and calculate $d$ :

$d = 16 - 5$

$d = 11$