A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?
(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.
(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.
Yes, you are right about the following two equations:
15x = Gross Revenue in one week from oranges
18g = Gross Revenue in one week from grapefruit
However, this doesn't give us enough information to answer the question. Let me explain why that is!
To keep things simple, let's use Rx to refer to revenue from oranges, and Rg to refer to revenue from grapefruit. So we have the following 3 equations:
15x = Rx
18g = Rg
x = 2g + 20
Here, we have 3 equations, and four different variables (also called "unknowns"): x, g, Rx, and Rg.
Happy to help! Let's take another look at Statement 1:
"Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped."
So we are told that the number of oranges shipped (we'll call that x) is 20 more than twice the number of grapefruits shipped (we'll call that g).
Using these variables, your equation is correct:
x = 2g + 20
However, we can't really say anything about the revenue at this point. We know that the farmer gets $15 per crate of oranges, and and $18 per crate of grapefruit. So we know that the revenue from oranges will be x*15, and the revenue from grapefruits will be g*18.
However, we cannot say that x*15 = revenue. You have to be careful here! x*15 = revenue from oranges, but not revenue from grapefruits.
Here, we cannot make any further equations. We could take:
x*15 = revenue from oranges
And plug in x = 2g + 20, to get
(2g + 20) * 15 = revenue from oranges
But this won't help us, because we don't what the revenue from oranges has to be equal to.
The full text of the problem should be visible here. Since these are official problems, though, you can find them on other sites through Google as well. I just copy and paste the first sentence in quotes and several websites pop up with the full text. Hope that helps!
3 Explanations