Question

Jeff has $1.35 in nickles and dimes. He has a total of 15 coins. How many of each coin does he have?
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Answer 1

For this case we propose a system of equations.

We know that a dime equals 10 cents and a nickel equals 5 cents.

So:

x: Let the variable that represents the number of dimes

y: Let the variable that represents the number of nickels

According to the statement we have:

$x + y = 15\\0.10x + 0.05y = 1.35$

We multiply the first equation by -0.10:

$-0.10x-0.10y = -1.5$

We have the following equivalent system:

$0.10x + 0.05y = 1.35\\-0.10x-0.10y = -1.5$

We add the equations:

$0.10x-0.10x + 0.05y-0.10y = 1.35-1.5\\-0.05y = -0.15\\y = \frac {-0.15} {- 0.05}\\y = 3$

So, Jeff has 3 nickels

$x + y = 15\\x + 3 = 15\\x = 15-3\\x = 12$

Jeff has 12 dimes.

Answer:

12 dimes and 3 nickels