Bunuel wrote:

Tough and Tricky questions: Word Problems.

A swim club that sold only individual and family memberships charged $300 for an individual membership. If the club’s total revenue from memberships was $480,000, what was the charge for a family membership ?

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.

(2) The club sold 1.5 times as many family member- ships as individual memberships.

Kudos for a correct solution.x+y=480,000

x= total revenue from individual memberships = Individual Memberships [i] * Individual Rate [r1]

y= total revenue from family memberships = Family Memberships [f] * Family Rate [r2]

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.x= \(\frac{1}{4}\)*$480,000 = $120,000

x= i * r1 = i*$300 = $120,000 ==> i= 400 individual memberships

y= \(\frac{3}{4}\)*$480,000 = $360,000

y= f * r2 ==> two unknown variables, hence

Not Sufficient.

(2) The club sold 1.5 times as many family member- ships as individual memberships.x+y = $480,000; and r1=$300 ==> (i * $300) + (f * r2) = $480,000, where f = \(\frac{3}{2}\)i

(i * $300) + (f * r2) = (i*$300)+(\(\frac{3}{2}\)i*r2) = $480,000 ==> We still have two unknown variables and one equation, hence

Not sufficient.

(1) + (2)(1) i=400 memberships; and y=$360,000

(2) f= 1.5i = \(\frac{3}{2}\) * 400 = 600 family memberships

y= $360,000 ==> y = f*r2 ==> 600 * r2 = $360,000

r2=$600, thus

Sufficient, Answer is C.