The Importance of Organization for Word Problems

red and white roller coaster on railings

Photo by Min An on Pexels.com

Let’s start with this challenging question:

Molly worked at an amusement park over the summer.Every two weeks she was paid according to the following schedule:at the end of the first two weeks she received $160.At the end of each subsequent two week period she received $1, plus an additional amount equal to the sum of all the payments she had received in the previous weeks.How much money was Molly paid during full 10 weeks of summer?

A. 644
B. 1288
C. 1770
D. 2575
E. 3229

To start, let’s create a table just to lay out the general information first:

After 2 weeks —> $160

After 4 weeks —-> $1 + (all previous)

After 6 weeks —-> $1 + (all previous)

After 8 weeks —-> $1 + (all previous)

After 10 weeks —-> $1 + (all previous)

Then fill in what the “all previous” would mean:

After 2 weeks —> $160

After 4 weeks —-> $1 + $160 = $161

After 6 weeks —-> $1 + ($160 + $161) = $161 + $161

After 8 weeks —-> $1 + ($160 + $161 + $161 + $161) = $161 + $161 + $161 + $161

After 10 weeks —> $1 + (all previous) = eight $161’s

At this point we can see that “all previous” is going to equal the initial $160 + seven $161 and then we’re adding $1 to it, so it’s really just $161 x 8 = $1288

We have an interesting sequence:

After 2 weeks —> $160

After 4 weeks —-> one $161

After 6 weeks —-> two $161

After 8 weeks —-> four $161

After 10 weeks —-> eight $161

Basically the “number” of $161’s just doubled from 4 weeks to 10 weeks.

Now to add them all up, again, we’re just going to count up all of the number of $161’s.

We have our initial $160 + 15*($161) = $2575. The correct answer is (D).

You will see over and over again that it’s not the Math calculations in Word Problems that will trip you up, but the inability to be super organized on your scratch paper. 🙂