SAT Question of the Day Explained – October 7, 2014 – Math, Ratios, Proportions

Today’s SAT question of the day is a math question that’s an excellent example for any test taker to review.  One brother earns 10 dollars for each lawn he mows, while the other brother gets 3 of those dollars for each lawn with which he helps.

In other words, one brother (d) earns 10 dollar per yard, while the other (t) earns 3 dollars per yard.

Whenever you can find a per statement, you know you can make a ratio…and with two related ratios, we can make a proportion.

The first brother can be represented by d/10, 10 dollars per d yards.  The second, t/3, 3 dollars per t yards.  Since we’re ultimately trying to relate these to each other and find d in terms of t (since all the answer choices begin with “d =”), let’s add an equal sign to make our proportion.

d/10 = t/3

Now, we can cross-multiply:

3d = 10t

And divide both sides by  3 to get d alone:

d = 10t/3