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 $n$ $n$ and the number of dimes $d$ $d$ .

From the problem we know:

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

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

Next, we solve the first equation for $d$ $d$

$n + d - n = 16 - n$ $n + d - n = 16 - n$

$d = 16 - n$ $d = 16 - n$

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

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

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

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

$- 0.05 n + 1.6 = 1.36$ $-0.05n + 1.6 = 1.36$

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

$- 0.05 n = - 0.25$ $-0.05n = -0.25$

$\frac{- 0.05 n}{- 0.05} = \frac{- 0.25}{- 0.05}$ $(-0.05n)/(-0.05) = (-0.25)/(-0.05)$

$n = 5$ $n = 5$

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

$d = 16 - 5$ $d = 16 - 5$

$d = 11$ $d = 11$