Ken bought 2 video games and 1 DVD for a total of $105. Jerome bought 1 video game and 4 DVDs for a total of $80. Which system o
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that is what the line will look like.
We want to compute
The goal is to write it in the following form:
First step: How many "copies" of does
contain? We can write
, so the answer is
copies.
If we distribute to
, we get
If we were done, then this product would have matched the numerator at the start. But it doesn't; there are still some terms that need to vanish. In particular, we still have to account for
Second step: How many copies of can we find in
? Well,
, so the answer is
. Then
but this still doesn't match the original numerator. We still have to deal with
Third step: How many copies of can we get out of
?
. Then
This also doesn't match the original numerator. We have a difference between what we have and what we want of
But we also can't divide into chunks of
, and we can't continue the division algorithm.
Our final answer would be
For the second problem, you should find