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| Math Central | Quandaries & Queries |
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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 $ \$5$, adults' admission costs $ \$8.$ I tried something like 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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