What this is saying is that when x = 4, y = 3. What happens if I double the x?
Well, if we double our x, we have to do the exact same thing to y in order to
maintain the proportion.
When you have to solve for a variable in a proportion, the simplest way is to use
a very powerful tool with a very boring name: “cross multiplication.” To cross
multiply, you turn the two fractions into a simpler equation by multiplying
diagonally across the equals sign. For example, if you have a proportion like:
You can solve for x by multiplying each denominator by the numerator on the
opposite corner, and setting those two expressions equal to each other.
Now let’s take a look at a more difficult problem:
At the jelly bean factory, the ratio of watermelon jelly beans to popcorn jelly
beans is 6:2. If 800 watermelon and popcorn jelly beans are manufactured per
day, how many watermelon jelly beans are manufactured per day?
The first step is to try to ignore the thought of how disgusting watermelon
jelly beans would taste when mixed with popcorn jelly beans. The second step is
to think of the given ratio as a relationship of part to part. For every six
watermelon jelly beans the factory makes, it makes two popcorn jelly beans. But
with the information given, we need to make a new ratio of part to whole, and
then set up a new proportion. To get the whole, we will add the two parts
together: 6 + 2 = 8. Now what is the ratio of watermelon jelly beans to all jelly
beans? 6:8, or 6/8. Let’s use that new ratio to set up a new proportion and solve:
Cross multiplying and solving for x will tell us the total number of watermelon
jelly beans: 600.