equations

Hi alltimeacheiver!

Let us first start by rephrasing the stem. Since we do not know the price per hotdog or the price per soda, we need variables:

h = $ of 1 hotdog
s = $ of 1 soda

The question then asks: what is (3h + 2s)?

This is a classic "Combo" problem. We could find the answer if we were ever able to solve for the price of each hotdog and the price of each soda separately, BUT we could also solve if we could build the combination (3h + 2s) from one of the answer choices.

Statement (1): We can translate this to: 5s < 2h

- We could try to simplify a bit: s < 2h/5 or 5s/2 < h, but we don't have a specific value to plug into the original combo. For example. I could say that 3h+2s = 3h+2(something<2h/5) but this result still has variables and really doesn't nail down a value. INSUFFICIENT

Statement (2): We can translate this to: 9h + 6s = 21.

- because everything has a common divisor (3) we should start by dividing that through: 3h+2s=7. Now remember what the original question asked - it wanted to know the value of 3h+2s, and we just found it!! 3h+2s=7.

- alternatively, we could have solved for either the h or the s and plugged into the "combo".
6s=21-9h
s=7/2 - 3h/2

Plug this back into the combo for s:
3h+2s = 3h+2(7/2-3h/2) = 3h+7-3h = 7

Because we were able to solve to a real number (no variable), this statement is SUFFICIENT.

The answer is B


I hope this helps!

Whit