Question

A collection of five coins has a value of $1 and consists of dimes and
quarters. How many of each type of coin are there?

Answer 1

For this case we propose a system of equations. We have to:

x: Let the variable that represents the number of dimes

y: Let the variable that represents the number of quaters

We know that:

One dime equals 10 cents, $0.10

A quater equals 0.25 cents, $0.25

According to the statement we have:

$x + y = 5\\0.10x + 0.25y = 1$

We multiply the first equation by -0.10:

$-0.10x-0.10y = -0.5$

We have the following equivalent system:

$-0.10x-0.10y = -0.5\\0.10x + 0.25y = 1$

We add the equations:

$-0.10x + 0.10x-010y + 0.25y = -0.5 + 1\\0.15y = 0.5\\y = \frac {0.5}{0.15}\\y = 3.33$

Approximately 3 quater coins

$x = 5-y = 5-3 = 2$

And two dimes

Answer:

3 quater

2 dimes