I don't know how to explain this to my soon to be 4th grader:

Question

There are 765 marbles in a bo.  There are twice as many blue marbles as green marbles.  There are 3 times as many red marbles as blue marbles.  How many red marbles are there in the box?

Answer 1

g represents the number of green marbles

2g represents the number of blue marbles (twice means two times)

3(2g) represents the number of red marbles (three times the blue)

 

g + 2g + 3(2)g = 756     sum of all marbles

g + 2g + 6g = 756         multiply

9g = 756                       combine

g = 84                          divide both sides by 9

 

Now use the definitions above to calculate the number of blue and red.

Answer 2

Jenna, try this ; There are 3 colored marbles in a box. The goal is to determine the number of marbles of each color. Tell your son that himself,  you, Jenna, Bam a gentleman from Columbus, Ohio, we don't know yet the answer. BUT, WITH SOME MATH FUN, WE ARE GOING TO FIND OUT!

 

Since nobody knows in advance the answer, we're going to pretend we know !!! That's the key !

 

Let's pretend that the number of red marbles is R ( between 1 and a million to add some excitement and drama ). Likewise, let's label B the number of blue marbles and G the number of green marbles. We're told that there are 765 marbles in the box.

 

IT IS OK TO SAY AND WRITE B + G + R = 765.

 

You may tell your son that this type of expression is called also an equation. We're also told in the word problem that we have "more" blue marbles than green marbles, exactly 2 blue for 1 green or half the amount of blue marbles is the exact amount of green.

 

IT IS OK TO SAY AND WRITE B = 2G or B/2 =G.

 

We're, lastly, told that the amount of red marbles divided by 3 is the exact amount of blue or , equivalently, 3 times the amount of blue marbles is exactly the amount of red marbles.

 

IT IS OK TO SAY AND WRITE R/3 = B or R=3B.

 

Now that we have 3 equations and 3 unknowns ( for few minutes) we are going to gently manipulate the system and see what happen! B + B/2 + 3B = 765 same as 2B + B + 6B = 1530 same as 9B=1530 same as B=170 which leads to G = 85 and R=510. VOILA! There are 510 red marbles in the box.