Mathnasium Number Sense and Fruit!

It's another Word Problem Wednesday, and we're back with a sweet little word problem designed to test your number sense! Solve today's word problem and check below for the answer.

A bunch of bananas and a cantaloupe together weigh 6 pounds. A papaya and a cantaloupe together weigh 5 pounds. A papaya and a bunch of bananas together weigh 4 pounds. Find the weight of each fruit.

This is an algebra problem in disguise. It’s not like the sneaky fruit problems floating around Facebook and the internet where the drawing of fruits are subtly different, thus causing controversy that keeps the puzzling and arguing going. This is a typical Mathnasium problem and it is a bonafide algebra problem. And just to head off any argument, the bunch of bananas is considered a singular fruit.

There are several approaches to solving this problem. We could use systems of equations and it would pop out an answer quickly. But let’s use some intuition and discuss this the way we might approach it with an elementary student. Just for brevity, we’ll use the initials of each fruit.

Converting the problem into number sentences, we get:

B + C = 6 --- statement (1)
P + C = 5 --- statement (2)
P + B = 4 --- statement (3)

Since 6 = 5 + 1, if we diagram a balance beam, we could put statement (1) on one side and statement (2) on the other with an extra (1) pound and it would balance.

B + C = P + C + 1

Most students would agree with that statement. Then we can remove the cantaloupe from both sides and the balance beam should still balance.

B = P + 1 --- statement (4)

Now, we can substitute statement (4) into statement (3) and we’ll get:

P + P + 1 = 4

We have many graphical balance beam problems like this and our students can arrive with some trial and error that P = 1½. This is how we develop the intuition for abstractly manipulating equations.

Given that P = 1½, then from statement (4), B = 2½, and it follows that C = 3½. We teach ½ as early as Kindergarten and we have success with young elementary students being able to follow and understand the manipulation.

For our middle schoolers, we can explain systems of equation. The difference of statements (1) and (2) yields:

B - P = 1 -- statement (5), hey it's statement (4) rearranged!

The sum of statement (3) and (5) yields:

2B = 5

giving B = 2½, that it follows from (1) and (3) that C = 3½ and P = 1½.

If you need more help understanding this reasoning, please feel free to stop by our store and ask. We'll be happy to help.

Contact:
Ruby Yao and Benedict Zoe
www.mathnasium.com/fortlee
201-969-6284 (WOW-MATH)
fortlee@mathnasium.com
246 Main St. #A
Fort Lee, NJ 07024

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