Question

To ship Liam's package, National Parcel charges a $15.76 flat fee and $1.53 per pound. To ship the same package, Statewide Shipping charges a $19.48 flat fee and $1.29 per pound. How many pounds must Liam's package weigh for National Parcel's total charge to be the same as Statewide Shipping's total charge? a. Analyze the given information. Write the general structure of the equation. b. Formulate a plan. Write the two variable expressions and define the given variable. Then, write the equation. Variable definition: Left-side expression:Right-side expression: Write the equation: Determine a solution. Solve the equation, Write the solution in a complete sentence with appropriate units. d. Justify the solution. Check the solution using substitution. B. Evaluate the reasonablonass of the solution and the problem-solving process. Is the solution rossonable?

Answer 1

Answer : 15.5 pounds

To ship Liam's package using National parcel

The flat fee rate is $15.76

Let x be the weight of the items in pounds

THey charged $1.53 per pound

Total cost = flat rate charge + charge per pounds x the weight in pounds

Total cost = 15.76 + 1.53 * x

Total cost = 15.76 + 1.53x -------------- equation 1

Using Statewide shipping

It charges a flat fee of $19.48 and $1.29 per pound

Total cost = flat rate charge + charge per pounds x the weight in pounds

Total cost = 19.48 + 1.29 * x

Total cost = 19.48 + 1.29x --------------- equation 2

To calculate how many pounds Liam's package weigh for National Parcel's total charge to be the same as Statewide Shipping's total charge, then, we need to equate the both equation

Equate equation 1 and 2

15.76 + 1.53x = 19.48 + 1.29x

Collect the like terms

19.48 - 15.76 = 1.53x - 1.29x

3.72 = 0.24x

Divide both sides by 0.24

x = 3.72 / 0.24

x = 15.5 pounds

The amount of pounds must Liam's package weigh for National Parcel's total charge to be the same as Statewide Shipping's total charge is 15.5 pounds