Q69. - Algebra 2

Question

For the exercise 69, define a variable, write an equation, and solve the problem.

 

BUSINESS A trucking company is hired to deliver 125 lamps for $\backslash (12$each. The company agrees to pay $\backslash )45$ for each lamp that is broken during transport. If the trucking company needs to receive a minimum payment of $\$1364$ for the shipment to cover their expenses, find the maximum number of lamps they can afford to break during the trip.

Step-by-Step Solution

Answer

The required answer is 3 approximately.

Step 1- Determine the total money that will be earned by the company

Calculate the money that will be received after successful delivery of lamps.

$125·12=1500$

Step 2- Define the required variable

Consider x be the count of affordable lamps. 

Step 3 – Form the equation

Take the variable and form the equation by using that 45 times of count of affordable lamps plus minimum payment is equal to the total money.

$45x+1364=1500$

Step 4- Solve the equation for x

Perform subtraction of 1364 from both sides of the equation.

$\begin{array}{c}45x+1364-1364=1500-1364\\ 45x=136\end{array}$

Perform division of 45 from both sides of the equation.

 

$\begin{array}{c}\frac{45x}{45}=\frac{136}{45}\\ x\approx 3\end{array}$

Step 5- Perform the checking

Perform the addition between the price of affordable lamps and minimum payment.

$3·45+1364=1500$

This results in the total payment which means that the obtained answer is correct.