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Chapter 5: Q. 250 (page 658)

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

A cashier has 54 bills all of which are \(10 or \)20 bills. The total value of the money is $910. How many of each type of bill does the cashier have?

Short Answer

Expert verified

The number of $10 bills are 17 and number of $20 bills are 37.

Step by step solution

01

Step 1. Given Information 

The given data is that a cashier has 54 bills all of which are $10 or $20 bills. The total value of the money is $910.

02

Step 2. Calculation  

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

Total value of money is $910 which can be expressed in the equation form as 10x+20y=910--(1)

Total number of bills is 54 that isx+y=54--(2)

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

10(x+y)=10(54)10x+10y=540--(3)

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

role="math" localid="1647707919211" 10x+20y-10x-10y=910-54010y=370y=37

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

role="math" localid="1647707905010" x+37=54x=17

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