Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Isabelle flew home from vacation with a heavy bag. With the first airline she flew, Isabelle had to pay $31 to check her bag, plus $5 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Isabelle had to pay $8 per pound that her bag was over the weight limit, in addition to the checked bag fee of $16. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag? Each airline's fee was $_____, and the bag was _____ pounds over the weight limit.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Isabelle flew home from vacation with a heavy bag. With the first airline she flew, Isabelle had to pay $31 to check her bag, plus $5 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Isabelle had to pay $8 per pound that her bag was over the weight limit, in addition to the checked bag fee of $16. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?   Each airline's fee was $_____, and the bag was _____ pounds over the weight limit.

Bytelearn · Accepted Answer

Define x for bag weight:  Let x be the number of pounds Isabelle's bag was over the weight limit. Write equations for the fees charged by each airline. Write fee equations:  Set the two equations equal to each other to find x. Set equations equal:  Solve for x by isolating it on one side of the equation. Solve for x:  Substitute x = 5 back into either original equation to find y, the total fee.

Full solution

More problems from Solve a system of equations using substitution: word problems

Related topics