We can buy x apples for n dollars.
How many apples can we buy with m dollars?
We do need to set this up as a proportion, and the thing about a proportion is just being
careful about how we do it.
So we can buy x apples for n dollars.
How many apples - that means we do not know the number of apples, so I will put that on
top since apples were on top on the left side of the proportion - how many apples can we
buy with m dollars?
So let's step back and take a look at this proportion.
The left-hand side has to do with what we knew to begin with.
They both match in that way.
The right-hand side of the proportion stands for the new situation, so that all matches.
On the top, we have apples on both the left and the right, and on the bottom we have dollars
on both the left and the right.
So the proportion is acceptable.
We have x over n equals the question mark over m.
I'm rewriting it so that it will be a little easier to look at without the labels.
The labels were an important part in helping us to set up the proportion correctly, but
we don't need them anymore.
At this point we want to solve for the question mark, so if you remember about proportions,
in order to solve them, you will take the upper left times the lower right, and set
that equal to the lower left times the upper right.
Finally you will divide by the number that is keeping your question mark from all alone.
And we discover that xm over n will describe the number of apples that we can buy with
m dollars.
OK, second problem.
We can drive y miles on x gallons of gas.
How many gallons will we need to go z miles?
Let's go ahead and set up our proportion.
We can drive y miles - I'm going to put that down first because it came to me first - y
miles on x gallons.
How many gallons - that means the question mark has to go down here with gallons - will
we need to go z miles?
So once again, just checking out the proportion to see if it is acceptable - these both have
to do with the original situation.
These both have to do with the new situation.
Both of the phrases on the top have to do with miles, and both on the bottom have to
do with gallons.
It looks good.
Let's rewrite it without all the labels.
Now let's multiply y times our question mark, set that equal to x times z, solve for the
question mark by dividing by y on both sides, and we discover that the result is xz over
y, which describes how many gallons we will need to go z miles.
2