My 7th graders are working on “percent of” problems, and late last night, I came across this gem in 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 at first. Then immediately thought, Fawnzie, since when do you use algebra to solve stuff like this? C’mon, do your rectangles.
So, I think of 40% as 2 out of 5 boxes:
That means 75 olives are split into 5 groups of 15 → so 2 groups (30 olives) are green.
Now I’ve eaten some of the green olives until only 10% of the remaining olives are green.
But I didn’t touch the 45 black olives. So those 45 olives now make up 90% of what’s left. That must be 9 groups of 5 → each group is 5 olives.
Which means only 5 green olives remain. Started with 30, now have 5. So I ate 25 green olives.
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?
I'd rather use the drawings to walk through this than show the algebra.
