Question

Ellie, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of $10 plus $3 per kilogram. The second charges $7 plus $6 per kilogram. Ellie 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

Ellie's package weighs 1 kilogram, and the cost to ship the package with either courier is $13.

Step-by-step explanation:

To find the weight of Ellie's package where the costs of two couriers are equivalent, we set up an equation where the two cost expressions are equal. Let x represent the weight of the package in kilograms.

The cost of the first courier is $10 + $3 per kilogram, so their cost expression is 10 + 3x. The cost of the second courier is $7 + $6 per kilogram, so their cost expression is 7 + 6x. To find the weight where the costs are the same, we set the two expressions equal to each other:

10 + 3x = 7 + 6x

Subtracting 3x from both sides, we get:

10 = 7 + 3x

Then, subtracting 7 from both sides, we get:

3 = 3x

Finally, dividing both sides by 3, we find that x is equal to 1:

x = 1 kg

Therefore, Ellie's package weighs 1 kilogram. To determine the cost for either courier, we substitute 1 kg back into any of the original cost expressions:

First courier: 10 + 3(1) = $13

Second courier: 7 + 6(1) = $13

Hence, the cost to ship the package with either courier is $13.

Answer 2

The weight of the package is 1 kilograms.

It will cost $ 13 by both the couriers services.

Step-by-step explanation:

Let the weight of her package is x kilograms

Now, according to the question:

The charges of first Courier = $10 + $3(x)

and The charges of Second Courier = $7 + $6(x)

Also, for x kilograms, both the charges are equal

⇒ $10 + $3(x) = $7 + $6(x)

or, 10 + 3x = 7 + 6x

or, 10 -7 = 6x - 3x

⇒ 3x = 3, implies x = 3/3 = 1

⇒ The weight of the package is 1 kilograms.

It will cost : 10 + 3(1) = $ 13 = 7 + 6(1) by both the couriers services.