Question

In the following exercises, translate to a system of equations and solve.

A cashier has 30 bills, all of which are \(10 or \)20 bills. The total value of the money is $460. How many of each type of bill does the cashier have?

Short answer

The number of $10 bills are 14 and number of $20 bills are 16.

Step-by-step solution

Step 1. Given Information 

The given data is that a cashier has 30 bills, all of which are $10 or $20 bills. The total value of the money is $460.

Step 2. Calculation  

Let number of $ 10 bills be x and number of $ 20 bills be y.

Total value of money is $460 which can be expressed in the equation form as $10x+20y=460--\left(1\right)$

Total number of bills is 30 that is $x+y=30--\left(2\right)$

Multiply equation (2) with number 10 and write the revised equation.

$$\begin{gathered} 10(x+y)=10\left(30\right) \\ 10x+10y=300--\left(3\right) \end{gathered}$$

Solve the equation (3) and (1) by subtracting equation (3) from equation (1).

$$\begin{gathered} 10x+20y-10x-10y=460-300 \\ 10y=160 \\ y=16 \end{gathered}$$

Substitute the value of y in equation (2) to find the value of x.

$$\begin{gathered} x+16=30 \\ x=14 \end{gathered}$$