Each are of quarters and nickels is worth $3.70. There are 22 coins in all How many of there?

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Answer 1 · 2017-01-09T14:49:50

First, let's call the number of nickels we have $n$ $n$ and the number of quarters $q$ $q$ .

Now we can write two equations which we can use to solve the problem through substitution:

First we know there are 22 coins in total, therefore:

$n + q = 22$ $n + q = 22$

And we know their value is $3.70 so we can write:

$0.05 n + 0.25 q = 3.70$ $0.05n + 0.25q = 3.70$

Step 1) solve the first equation for $n$ $n$

$n + q = 22$ $n + q = 22$

$n + q - q = 22 - q$ $n + q - color(red)(q) = 22 - color(red)(q)$

$n + 0 = 22 - q$ $n + 0 = 22 - color(red)(q)$

$n = 22 - q$ $n = 22 - q$

Step 2) Substitute $22 - q$ $22 - q$ for $n$ $n$ in the second equation and solve for $q$ $q$ .

$0.05 (22 - q) + 0.25 q = 3.70$ $0.05(22 - q) + 0.25q = 3.70$

$(0.05 \times 22) - (0.05 \times q) + 0.25 q = 3.70$ $(0.05 xx22) - (0.05 xx q) + 0.25q = 3.70$

$1.1 - 0.05 q + 0.25 q = 3.70$ $1.1 - 0.05q + 0.25q = 3.70$

$1.1 + 0.25 q - 0.05 q = 3.70$ $1.1 + 0.25q - 0.05q = 3.70$

$1.1 + (0.25 - 0.05) q = 3.70$ $1.1 + (0.25 - 0.05)q = 3.70$

$1.1 + 0.20 q = 3.70$ $1.1 + 0.20q = 3.70$

$1.1 - 1.1 + 0.20 q = 3.70 - 1.1$ $1.1 - color(red)(1.1) + 0.20q = 3.70 - color(red)(1.1)$

$0 + 0.20 q = 2.60$ $0 + 0.20q = 2.60$

$0.20 q = 2.60$ $0.20q = 2.60$

$\frac{0.20 q}{0.20} = \frac{2.60}{0.20}$ $(0.20q)/color(red)(0.20) = 2.60/color(red)(0.20)$

$(color(red)(cancel(color(black)(0.20)))q)/cancel(color(red)(0.20)) = 13$

$q = 13$

Step 3) Substitute $13$ for $q$ in the solution to the first equation in Step 1.

$n = 22 - 13$

$n = 9$

Solution:

There are 9 nickels and 13 quarters