Question

Chris buys 2 identical bags of cherries to make a pie.

There are more than 10 but less than 30 cherries in each bag.
Chris eats 7 cherries, then uses half of the rest in his pie.
Chris uses 11.5 cherries for his pie.
How many cherries were in each bag to start with?

Answer 1

Answer: 15

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Explanation using mental math:

He uses 11.5 cherries for his pie, which is half the amount left (after eating those 7 cherries).

This means 2*11.5 = 23 cherries were left over after he ate those seven. In other words, half of 23 is 11.5

If we reverse time, then we get those 7 cherries back to get 7+23 = 30 cherries total. Divide those up equally between the two bags and we get 30/2 = 15 cherries per bag.

Going forward in time we have 15 cherries per bag, so 2*15 = 30 total. He eats 7 to be left with 30-7 = 23 cherries. That cuts in half to 23/2 = 11.5 cherries for his pie.

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Explanation using algebra

c = number of cherries in each bag.

10 < c < 30 based on the second sentence

2c = number of cherries total from both bags combined

2c-7 = the amount left after Chris eats those 7 cherries

(2c-7)/2 = he uses half of the remaining cherries for the pie

Set that equal to the 11.5 number stated and solve for c.

(2c-7)/2 = 11.5

2c-7 = 11.5*2

2c-7 = 23

2c = 23+7

2c = 30

c = 30/2

c = 15

We effectively follow similar steps as when we did the mental math route.

Notice how c = 15 makes 10 < c < 30 true.