A bag contains mangoes that are either green or yellow. The ratio of green mangoes to yellow mangoes in the bag is 3 to 5. When two green mangoes are removed and ten yellow mangoes are added, the ratio becomes 2 to 5. How many green mangoes were originally in the bag?

Say that the original number of green mangoes is *g* and the original number of yellow mangoes is *y*. So you know that .

When two green mangoes are removed, and 10 yellow mangoes are added, the ratio becomes .

Now we have two equations and two variables—we can solve for *g* to get the answer we seek!

Manipulate the first equation to set it equal to *y*:

Now substitute into the other equation:

You can check your work on this easily enough. If there were originally 18 green mangoes and the ratio of green to yellow was 3 to 5, then there were originally 30 yellow mangoes. What happens if you take away 2 green mangoes and add 10 yellow mangoes? You end up with 16 green and 40 yellow, which simplifies to a ratio of 2 to 5, just like the question said.

One last note here. You didn’t provide answer choices for this question so I assume there weren’t any. However, if there *were* answer choices here, this would be an ideal question to backsolve—essentially to “check your work” like we just did in the last paragraph without doing the work!

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