Twenty gallons of crude oil were poured into
two containers of different size. Express the amount of crude oil poured into the smaller container
in terms of the amount g poured into the larger container.
The expression they're looking for is found by
this reasoning: There are twenty gallons total, and we've already poured g gallons of
it. How many gallons are left? There are 20
– g gallons left. They want the answer
"20 – g".
This is the "how much is left" construction:
You will be given some total amount. Smaller amounts, of unspecified sizes, are added (combined,
mixed, etc) to create this total amount. You will pick a variable to stand for one of these unknown
amounts. After having thus accounted for one of the amounts, the remaining amount is whatever is
left after deducting this named amount from the total.
They may tell you that a trip took ten hours,
and that the trip had two legs. You might name the time for the first leg as "t",
with the remaining time for the second
leg being 10 – t.
They may tell you that a hundred-pound order of
animal feed was filled by mixing products from Bins A, B, and C, and that twice as much was added
from Bin C as from Bin A. Let "a" stand for the amount from Bin A. Then the amount from Bin
C was "2a", and the amount taken from Bin B was the remaining portion
of the hundred pounds: 100 – a
I'm making a big deal about this "how much
is left" construction because it comes up a lot and tends to cause a lot of confusion. Make
sure you understand this one!
Once you've learned to translate phrases into expressions
and sentences into equations, you are ready to dive into word problems. Of course, there are infinitely-many
possible word problems (physics is all word problems; business math is all word problems; "real
life" can feel like an essay question...). The following links lead to explanations and examples
of some basic types of word problems that you can expect to see in your classes: