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Question

the smith family and the jackson family are having there basements remodled the smiths contractor charges 16.50 per hour plus 289 in supplies the jacksons contractor charges 18.75 per hour plus 274.60 for supplies at how many hours of work will the total cost be the same for both families

Answer 1

Let's make this into an algebra problem where "X" represents what we want to solve for: hours of work.

First the Smiths:

289+16.50X

Now the Jacksons:

274.60+18.75X

All we have to do now is set them equal to each other and solve. That will tell us how many hours of work are needed for the costs to be the same.

289+16.50X=274.60+18.75X [Here's our equation]

289=274.60+2.25X [Subtracted 16.50X from both sides to get our "X" on only one side.]

14.4=2.25X [Subtracted 274.60 from both sides to isolate X on the right side.]

6.4=X [Divided both sides by 2.25 to get the X alone.]

X=6.4 hours [Flipped the equation around to make it look nice. There's your answer.]

Now we can plug it in to the original equation to check our work.

289+16.50(6.4)=274.60+18.75(6.4)

289+105.6=274.6+120

394.6=394.6

Looks good!