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To find the updated total future earnings, we're going to start by writing down the
initial total future earnings we had. So, this is our baseline, this is what we
start out with, and now, I'm going to show how these two changes affect the equation.
The first thing that happens is that Mr. Belvedere triples the amount of money that
Grant will eventually make off of these first orders. So, that means we need to
multiply this quantity, 84w+60n, by 3. So I'm going to have to put parentheses
around it and write a 3 out front. Great. Then the 2nd step is that a
school orders, one set of wipers and one pair of nozzles for each of its 150
students. So that means that for one student, the school wants one wiper set
and two nozzles since they're a pair of nozzles. And we know that one wiper set
costs w dollars, so for one student, the school is going to pay w plus the cost for
the two nozzles, which we know is 2n. So the school pays w+2n for every student.
However, they have 150 students to pay for, so that means that the amount the
school will pay is 150(w+2n), so this is our final equation. The updated total
future earnings will be equal to 3 times the quantity 84w+60n, and then,
added onto that, 150(w+2n) to account for the orders from the school. So looking
back at the quiz that you took, I'm sorry, I left out the word total from the quiz,
these are the same quantity. So we need to figure out which of these four choices
corresponds with or is equal to this expression up here and the correct answer
is this 4th choice. Now this doesn't look exactly like this equation, number
for number, and that's because the 150 has been distributed to the two terms inside
the parentheses. So, if we do that, we keep the first part of the expression the
same and then I just multiply 150 by either the terms in the parentheses, just
like you did with all of your practice using the distributive property. 150 times w is
just 150w and 150 times 2n is 300n. So that's why the final answer is the correct
choice. Great. Now, we're one step closer to giving Grant a very nice and easy to
use equation for the amount of money he's going to earn.