Exam Pack 2 - ratios

The table above shows the quantities and prices per pound of three types of nuts that are combined to make a nut mixture. The mixture contains twice as many pounds of cashews as pounds of almonds, and 3 times as many pounds of walnuts as pounds of almonds. What is the cost of the mixture, in dollars, expressed in terms of a?

A) 4a
B) 6a
C) 13.5a
D) 20.5a
E) 24.5a

Let a = 1 pound of almonds.
Since almonds cost $4 per pound, the total cost of the almonds = $4.

The mixture contains twice as many pounds of cashews as pounds of almonds.
Thus, the weight of the cashews = 2*1 = 2 pounds.
Since cashews cost $3.50 per pound, the total cost of the cashews = (2)(3.5) = $7.

The mixture contains 3 times as many pounds of walnuts as pounds of almonds.
Thus, the weight of the walnuts = 3*1 = 3 pounds.
Since cashews cost $4.50 per pound, the total cost of the walnuts = (3)(4.5) =$13.50.

Total cost of the entire mixture = 4 + 7 + 13.5 = $24.50. This is our target.
Now plug a=1 into the answers to see which yields our target of $24.50.
Only E works:
24.5a = (24.5)(1) = 24.50.

The correct answer is E.

lucas211 wrote:Hello BTG

Tried plugging in numbers on the following question, but I can not get the right answer.
Help to this approach, and other approaches would be appreciated.

thanks in advance

And there's always good old-fashioned algebra.

If we have 'a' pounds of almonds and twice as many cashews, we'll have '2a' pounds of cashews.

If we have 'a' pounds of almonds and three times as many walnuts, we'll have '3a' pounds of walnuts

Cost of cashews = 2a * 3.50 = 7a
Cost of almonds = a * 4 = 4a
Cost of walnuts = 3a * 4.5 = 13.5a
Total cost = 24.5a

(Also note that the cost of cashews and walnuts alone is 7a + 13.5a = 20.5a. Once you realize that the cost is more than 20.5a, you're done.)