For every seven bags, Isabella has
five pairs of shoes. What is the ratio of the bags to
the total number of bags and shoes?
Here, we’re looking for a ratio and
we know that a ratio is a comparison of two different quantities. When solving ratio problems, we
always need to carefully identify what quantities we are comparing. Our ratio will be of the bags to
the total number of bags and shoes. Our first value is the number of
bags, but our second value will be the number of bags and shoes together. We know that for every seven bags,
Isabella has five pairs of shoes. We can write seven in place of the
number of bags. But for the total, we’ll need seven
and then five. Seven plus five is 12. This ratio is then seven to 12.
Again, the key to solving this
problem is correctly identifying what each piece of the ratio is. We knew that the first piece
represented the number of bags Isabella had. But we had to know that the second
piece, the second quantity we were comparing, were bags and shoes, a total value,
which required an additional step of adding the shoes and the bags. When we look at seven and 12, they
do not have any common factors apart from one. And therefore, seven to 12 is in
its simplest form.