Question

Lillian’s has $3.80 in nicole’s and quarters in her backpack. She has 22 more nickels than quarters. How many coins of each type does she have?

Answer 1

Question: Liliana has $3.80 in nickels and quarters in her purse. She has 22 more nickels than quarters. How many coins of each type does she have?

Solution:

Liliana has $3.80 in nickels and quarters in her purse.

She has 22 more nickels than quarters.

We first have to establish a system of equations. Since we have two unknown variables, we need to have two equations. The first equations;

let x = number of quarters

x+22 = number of nickels

The total worth of coins = $3.80

The value of a quarter is $0.25 and the value of a nickel is $0.05.

According to the problem:

`0.25x+0.05(x+22)=3.80`

Applying the distributive property, we get:

`0.25x+0.05x+1.1\text{ = 3.80}`

this is equivalent to:

`0.25x\text{ +0.05x = 3.80}-1.1`

this is equivalent to:

`0.3x=2.7`

Solving for x, we obtain:

`x=\text{ }(2.7)/(0.3)=9`

Thus, we obtain that:

The number of quarters = x = 9

number of nickels = x+22 = 9+22 = 31

So t