SAT Question of the Day August 11th 2013

If Kelly buys t pens priced at 2 dollars each and u pens priced at 4 dollars each, which of the following expresses, in terms of t and u, the average (arithmetic mean) price, in dollars, of these pens?

A.     (3 times t) + (3 times u) over (t + u)

B.     (3 times t) + (3 times u) over (t imes u)

C.     (3 times t times u) over (t + u)

D.     ((2 times t) + (4 times u)) over (t + u)

E.     ((2 times t) + (4 times u)) over (t times u)

Very similar to the question discussed in the previous post, we have a word to equation problem.

One way (not recommended) is plug in and see that you obtain the number you expect to get.

The better way, in my opinion, is to try and translate the problem.

Lets say Kelly buys 4 pens, each for $2. She will pay for them $8. If she buys the other kind, lets say 5 of them, she will pay for each $4 and for these $4 pens she’ll pay $20.

She bought 9 pens for a total of $28.

Each pen, on average, will cost $28/9 which is a little less than $3.5

This is the way to calculate a weighted average (where we care about the amount we have of each ingredient).

If we follow the steps we just took using the letters t and u instead of the actual numbers it is clear we should mark D.

68% got it right.

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