Question

Naomi, an office manager, needs to find a courier to deliver a package. the first courier she is considering charges a fee of $19 plus $3 per pound. the second charges $5 plus $4 per pound. naomi determines that, given her package's weight, the two courier services are equivalent in terms of cost. how much will it cost? what is the weight?

Answer 1

When the courier services charge the same, the package weight is 14 pounds, and the total cost for delivery is $61.

Step-by-step explanation:

To determine the cost and weight when the two courier services charge the same, we can set up an equation where the first courier's charge ($19 + $3 per pound) equals the second courier's charge ($5 + $4 per pound). Let the weight of the package in pounds be represented by w.

The equation can be written as: $19 + 3w = $5 + 4w. To find w, we deduct $19 from both sides of the equation and simplify.

Subtracting $19 from both sides gives us: 3w = $5 + 4w - $19. This reduces to 3w = 4w - $14. We then subtract 4w from both sides to get: -w = -$14. We find that w equals 14 pounds when the fees are equivalent.

To calculate the exact cost, we can substitute the weight back into either courier's pricing formula. Using the first courier's charges, the cost would be $19 + ($3 × 14) = $19 + $42 = $61.