My 7th graders are working on “percentages of” problems currently, and late last night, I saw this problem on one of Don Steward’s handouts.

There are 75 olives, 40% of which are green. I eat some of the green olives until 10% of the olives that remain are green. How many green olives did I eat?

How would you solve this?

I solved it using algebra. Then, immediately, I thought, *Fawnzie, since when do you use algebra to solve stuff like this. C’mon, do your rectangles*.

I think of 40% as 2 of 5 boxes.

So, 75 olives must split into 5 groups of 15, so there are 30 green olives.

Then, I ate some olives to end up with only 10% of the remaining olives are green.

Well, since I didn’t eat any of the 45 black olives, so these 45 must make up 90% of the olives remaining [in the 9 boxes], so 45 must split into 9 groups of 5.

Oh, look! I began with 30 green olives, I now only have 5 green ones left, so I must have eaten 25 of them.

Okay, your turn.

There are 80 olives, 75% of which are green. I eat some of the green olives until 20% of the remaining olives are green. How many green olives did I eat?

Because if I tried to show my kids the work below, or versions thereof, a few might just shit in their pants.

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