Math: 628300a9

ID: 628300a9

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Organize and conquer.

Method 1: Because there is no restriction that says that both of experiments A and B must be conducted, we can effectively ignore B and focus on A, the one to which the unknown x is attached. If experiment A requires 6 teaspoons of salt and there can be no more than 5 stations, that means there can be no more than 6 * 5, or 30 teaspoons used. Check the answer choices to eliminate anything possible, plugging in 5 for x.

A. 5(5) = 25 X

B. 10(5) = 50 X

C. 2(5) + 20 = 30 √

D. 10(5) + 20 = 70 X

The correct answer is (C), and the solution takes less than 30 seconds as long as you have a decent grasp of arithmetic. Had two answer choices worked, you could easily drop x from 5 to, say, 4 and think of the other station as one that used 4 teaspoons of salt (for experiment B). Only (C) would yield 28, the same as 6 * 4 + 4 * 1 (6 tsp * 4 stations + 4 tsp * 1 station).

Method 2: With a little creativity, you can put Desmos to use. Let x be less than or equal 5, then test the answer choices.

Now remember, x represents the number of stations set up for experiment A, which requires 6 teaspoons of salt. Thus, if all stations were set up for experiment A, there would be 6 * 5, or 30 teaspoons of salt required, and the purple line clearly shows this point. The blue line shows a nonsensical 25 teaspoons, which cannot be derived from any combination of 6 or 4 teaspoons (for experiment B); the green line shows 50 teaspoons, which would be accurate if there were 5 stations each set up for A and B, ignoring the given not both at the end of the second line of the passage; and the black line is so high that it defies logic. The correct answer must be (C).

Method 3: Your math teacher or textbook might work through the following solution. If there are 5 stations and each will be set up for experiment A or B, then we know that A + B = 5. If, as the question stem tells us, x stations are set up for A, then we can alter our equation into an expression:

(x) + (5 - x)

To track teaspoons of salt, if each A setup requires 6 teaspoons and each B setup requires 4 teaspoons, then we now have a way to derive the answer.

6(x) + 4(5 - x) = total teaspoons

6x + 20 - 4x = total teaspoons

2x + 20 = total teaspoons

The correct answer is (C).