Proportion Word Problem

Q:  The ratio of the number of canoes for rent to the number of kayaks for rent is 8 to 5.  There are 20 kayaks for rent.  Write and solve a proportion to find the number of canoes for rent.


A:  The information from the problem tells me:

8 canoes for every 5 kayaks.  I can write this like a fraction:

8 canoes / 5 kayaks

Now, I know there are 20 kayaks and want to to find the canoes… So,

8 canoes / 5 kayaks = ? canoes / 20 kayaks

Putting this more mathematically (taking out the words):

8/5 = x/20

So, now we must solve for x (get x by itself)…. Currently, x is being divided by 20.  To “get rid of” the division, I will just multiply both sides by 20 to cancel it out like so:

(8/5)*20 = (x/20)*20

(Notice, this is the same as multiplying by 20/1 like so):

(8/5)*(20/1) = (x/20)*(20/1)

Multiply fractions across the top and across the bottom:

160/5 = 20x/20

And reduce:

32 = x.

The number of canoes is 32.

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