A store clerk sold 60 pair of
sneakers. The high-tops sold for 98 dollars
and 99 cents and the low-tops sold for 129 dollars and 99 cents. If the receipts for the two types
of sales totaled 6404 dollars and 40 cents, how many of each type of sneaker were
We’ve been given a lot of
information here. Let’s see if we can sort through
it. A total of 60 pair of sneakers were
sold. Two kinds of sneakers were sold:
high-tops and low-tops. Let’s just stop here.
We need to define some
variables. Let’s use an ℎ for the high-tops
that were sold and an 𝑙 for some low-tops that were sold.
One thing that we know is that all
the shoes that were sold added up to 60 pair. So if we add the high-tops that
were sold and the low-tops that were sold, they would equal 60 pair: ℎ plus 𝑙
equals 60. We also know that the high-tops
cost 98 dollars and 99 cents.
And that low- the low-tops cost 129
dollars and 99 cents, for a total amount sold 6404 dollars and 40 cents.
We can also write another
equation. We can write an equation that says,
the money spent on ℎ, the high-tops, plus the money spent on 𝑙, the low-tops,
equals 6404 dollars and 40 cents. But what goes here? How much money was spent on
The amount of money that high-tops
cost times the number of high-tops that were purchased, that’s how much money was
spent on high-tops, so we say 98 dollars and 99 cents times ℎ.
And we can do the same thing for
the money spent on the low-tops, the money that the low-tops cost multiplied by the
number of low-tops sold. So we say 129.99 times 𝑙.
Now we have two true equations
about the same situation. We wanna know what the intersection
of these two equations are, what makes both of these equations true. Let’s solve this problem through
Our first equation has a
coefficient of 98 dollars and 99 cents for ℎ, so we want our second equation to have
that same coefficient. Let’s multiply ℎ plus 𝑙 equals 60
by 98.99: 98.99 times ℎ, 98.99 times 𝑙, and 98.99 times 60, which equals 5939 and
Now what I have done is I’ve copied
down our first equation exactly how it was written. And now we wanna subtract our
second equation from the first equation. our ℎs are the same values, so they’ll
Next we subtract 98 dollars and 99
cents from 129 dollars and 99 cents. That leaves us with 31𝑙. We subtract 5939 dollars and 40
cents from 6404 dollars and 40 cents. And we’re left with 465.
Remember that our goal is to figure
out what ℎ and 𝑙 represent, so here we’ll need to get 𝑙 by itself. 31 is being multiplied by 𝑙. To move 31 to the other side, we’ll
need to divide both sides by 31. This tells us that the pairs of
low-tops sold were 15; 15 pairs of low-tops were sold.
Remember that a total of 60 pair of
sneakers were sold, so we can plug our 15 in for our equation ℎ plus 𝑙 equals
60. The number of high-tops sold plus
15 equals 60. We subtract 15 from both sides,
which tells us that ℎ, the number of high-tops sold, equals 45. High-top pairs: 45; low-top pairs: