Ann and Pierre purchased $37 worth of French fries.

Let orders of Ann be x and orders of Pierre be y, then

3x + 5y = 37

We are looking for x.

(1) 9x + 15 y = 111. It's a trap! If you combine the equations you will get nothing, since 3 x first equation = second equation. IS.
(2) x + y = 9 --> y = 9-x --> set in equation from question, SUFF.

B.

B

For the question that involves 2 equations and 2 variables, always check to see if you solve it from the equations.
3A + 5P = 37, if you multiply this by 3, you get (1) 9A + 15P = 111

CORRECT ANSWER IS B.

Let a be the number of orders that Ann purchased and let p be the number of orders that Pierre purchased. From the question stem, we can set up the equation 37 = 3a + 5p, which expresses the total cost of the French fries purchased by Ann and Pierre. In order to solve for the number of orders of French fries that Ann bought, we need to be able to set up another distinct equation that contains the variables a and p.

Statement (1): insufficient. From this information, we can write the equation 111 = 9a + 15b. We have another equation relating a and p, but is it distinct? No. Upon closer inspection, this is simply the result of multiplying both sides of the original equation 37 = 3a + 5p by 3. We can eliminate choices (A) and (D).

Statement (2): sufficient. From this statement, we can set up the equation 9 = a + b. Is this equation distinct from the original equation? Yes. This is therefore sufficient to find the value of a, or the number of orders of French fries that Ann purchased. Choice (B) is correct.

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