Red and Green Marbles
The ratio of red marbles to green marbles in a package is 3 to 5. 25 green marbles are in the package. What is the smallest number of marbles, and of which color, would you have to add to the package of marbles so that the ratio of red marbles to green marbles becomes 5 to 8?
(Source: Adapted from Mathematics Teaching in the Middle School, May 1994).
Investigation/Exploration of the Problem
We know the ratio of red to green marbles is 3 to 5. We can write this as a fraction like this:
We also know that there are 25 green marbles in the package. So we have to multiply 5 x 5 to get 25 green marbles. To keep the ratio in proportion, we have to multiply 3 by 5 to get 15 red marbles. (See below)
Red 3 x 5 = 15
Green 5 x 5 = 25
What is the smallest number of marbles we can add to the package of marbles so that the ratio of red marbles to green marbles becomes 5 to 8? We need to find a ratio such that the number of green marbles is at least 25. If we multiply 8 by 1, 2 ,or 3 we will not have enough green marbles, but if we multiply 8 by four we will have 32 green marbles. Since we multiplied the bottom by 4, we have to multiply the top number by 4 to keep the ratio in proportion. When we do this we see that our new ratio is 20/32 or 20 red marbles and 32 green marbles. So we need to add 5 red marbles and 7 green marbles to change the ratio of red to green marbles to 5 to 8.
Red 5 x 4 = 20
Green 8 x 4 = 32
Memorial Middle School