A shipping company charges a rate based on the weight of a package. The total cost C, in d… — ACT

A shipping company charges a rate based on the weight of a package. The total cost $C$ , in dollars, to ship a package of weight $w$ pounds is given by the formula $C = \frac{5}{8}(w - 2) + 6.50$ for packages weighing more than $2$ pounds. If the shipping cost for a certain package is $\$14.00$ , what is the weight of the package, in pounds?

Answer: 14 pounds

Answer

The weight of the package is 14 pounds.

Substituting

C = 14.00

into the formula gives

14.00 = \frac{5}{8}(w - 2) + 6.50

. Subtracting

6.50

from both sides yields

7.50 = \frac{5}{8}(w - 2)

. Multiplying both sides by the reciprocal

\frac{8}{5}

yields

12 = w - 2

. Finally, adding

2

to both sides gives the weight

w = 14

pounds.

Step-by-Step Solution

Substitute the total shipping cost into the formula.

14.00 = \frac{5}{8}(w - 2) + 6.50

Since the shipping cost

C

is given as

14.00

, we substitute this value into the formula to solve for the unknown weight

w

Subtract

6.50

from both sides of the equation.

7.50 = \frac{5}{8}(w - 2)

Subtracting

6.50

isolates the term containing the variable

w

on the right side of the equation.

Multiply both sides of the equation by the reciprocal of the fraction.

12 = w - 2

Multiplying by

\frac{8}{5}

eliminates the fractional coefficient of

\frac{5}{8}

on the right side.

Add

2

to both sides of the equation to solve for

w

w = 14

Adding

2

isolates the variable

w

, giving the final weight of the package.

Key Concept

Solving linear equations with fractional and decimal terms

Estimated Time:1m 30s

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