Question

A bag contains forty coins, all of them either 2 cent or 5 cent coins. If the value of the money in the bag is $1.55, how many coins of each kind are there?

Answer 1

See a solution process below:

Explanation:

First, let's call the number of 2 cent coins: `t`

Next, let's call the number of 5 cent coins: `f`

We can then write to equations from the information in the problem.

Equation 1: `t + f = 40`

Equation 2: `0.02t + 0.05f = 1.55`

Step 1) Solve the first equation for `t`:

`t + f = 40`

`t + f - color(red)(f) = 40 - color(red)(f)`

`t + 0 = 40 - f`

`t = 40 - f`

Step 2) Substitute `(40 - f)` for `t` in the second equation and solve for `f`:

`0.02t + 0.05f = 1.55` becomes:

`0.02(40 - f) + 0.05f = 1.55`

`(0.02 xx 40) - (0.02 xx f) + 0.05f = 1.55`

`0.80 - 0.02f + 0.05f = 1.55`

`0.80 + (-0.02 + 0.05)f = 1.55`

`0.80 + 0.03f = 1.55`

`0.80 - color(red)(0.80) + 0.03f = 1.55 - color(red)(0.80)`

`0 + 0.03f = 0.75`

`0.03f = 0.75`

`(0.03f)/color(red)(0.03) = 0.75/color(red)(0.03)`

`(color(red)(cancel(color(black)(0.03)))f)/cancel(color(red)(0.03)) = 25`

`f = 25`

Step 3) Substitute `25` for `f` in the solution to the first equation at the end of Step 1 and calculate `t`:

`t = 40 - f` becomes:

`t = 40 - 25`

`t = 15`

The Solution Is:

There are:

• 15 two cent coins

• 25 five cent coins