Problem Solving

swerve wrote:Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900

This REAL WORLD question requires us to find values that are positive INTEGERS.
So, for example, we can't have 1.3 boxes or 12.44 boxes.

Team A distributes 60% more boxes of booklets than Team B
Since we must have positive integers for these values, the SMALLEST possible numbers are as follows:
Team A: 8 boxes
Team B: 5 boxes

Team A has 60% fewer booklets per box than Team B
Since we must have positive integers for these values, the SMALLEST possible numbers are as follows:
Team A: 2 booklets per box
Team B: 5 booklets per box

In this case, the TOTAL number of booklets distributed by EACH TEAM is as follows:
Team A: (8)(2) = 16
Team B: (5)(5) = 25

So, the TOTAL = 16 + 25 = 41

Check the answer choices....nope, 41 is not an option.

Now recognize that multiples of 41 will also work.
For example, if each team sold TWICE as many boxes than they did in our first scenario, then the total would equal 82.
If each team sold 10 times as many boxes than they did in our first scenario, then the total would equal 410.
And so on.

When we scan the answer choices, we see that C (4100) is a multiple of 41.

Cheers,
Brent

swerve wrote:Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900

We can let the number of boxes of booklets distributed by Team B = b and thus the number of booklets distributed by Team A = 1.6b.

We can let the number of booklets per box for Team B = n and thus the number of booklets per box for Team A = 0.4n.

So the total number of booklets distributed is:

(1.6b)(0.4n) + bn = 0.64bn + bn = 1.64bn

Since b and n are integers, so is bn. Thus, we see we need to find an answer choice that results in an integer when divided by 1.64.

Since 4100 produces an integer when divided by 1.64, 4100 could be the number of booklets distributed by the two groups.

Answer: C