Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Justine, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of $20 plus $2 per kilogram. The second charges $10 plus $4 per kilogram. Justine determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?

Answer 1

• Weight: 5 kg

,

• Cost: $30

Step-by-step explanation

Let x be the weight of the package and y be the cost. For the first courier, we have that the cost is,

`y=20+2x`

And for the second courier,

`y=10+4x`

Justine determined that the two have the same cost, so we have to solve the system above. Using the elimination method, subtract the first equation from the second,

Add 10 to both sides of the equation,

`10=2x`

And divide both sides by 2,

`x=5`

Hence, the weight of the package is 5 kilograms.

To find the cost, replace x with 5 in any of the two equations,

`y=20+2x=20+2\cdot5=20+10=30`

The cost is $30.