   SEARCH HOME Math Central Quandaries & Queries  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 $\$5$, 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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.