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Question from Hannah, a student:

I am confused about a question on my homework, here is an example on what I need to do:

You own a sightseeing boat tour. Kids' admission costs , adults' admission costs \$8.
During that day you get (made-up number) \$521 with 71 admissions.
How many of each passenger boarded?

I tried something like
5x + 8y = 521
x + y = 71

But, I still don't understand how to solve it! Help?

Hi Hannah,

I am going to change your made-up number to \$523, then if x is the number of kids and y is the number of adults the equations become

5x + 8y = 523

x + y = 71

At this point multiply both sides of the second equation by 5 so the equations become

5x + 8y = 523

5x + 5y = 355

These equations can then be rewritten

5x = 523 - 8y

5x = 355 - 5y

Since both right sides are equal to 5x they must be equal and hence

523 - 8y = 355 - 5y

Solve for y.

This is probably not the way your textbook or teacher would present the solution. I expect they would multiply both sides of the second equation by 5 as I did to get

5x + 8y = 523

5x + 5y = 355

but the next step would be to "subtract the second equation from the first equation".

5x minus 5x is 0

8y minus 3y is 5y

523 minus 355 is 168

and hence subtracting the second equation from the first yields

3y = 168

Solve for y.

I hope this helps,
Penny

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