Question

Timothy sold 118 bottles of water at the baseball game. He sold them for $1.50 each. He decided to give 15% of the money he collected to a charity. How much money will Timothy give to the charity? Which explanation correctly tells how to check whether the answer is reasonable?

A.
Solution: $26.55

Explanation: If Timothy sells about 120 bottles of water, he will make about $180 (120 × $1.50).
Since Timothy wants to give 15% of this amount to charity, this would be about 0.15 × $180 or about $27.


B.
Solution: $162

Explanation: If Timothy sells about 120 bottles of water, he will make about $180 (120 × $1.50).
Since Timothy wants to give 15% of this amount to charity, this would be about $180 – $15 or about $165.


C.
Solution: $22.50

Explanation: If Timothy sells about 120 bottles of water, he will give the money he collects for 15 bottles to charity.
That means Timothy will give 15 × $1.50 or about $20 to charity.

Answer 1

The first solution is correct

The first solution does everything correctly, the approximated incoming is computed, and then the 15% of the rounded incoming is computed, i.e. the rounded incoming is multiplied by 0.15.

Let's see why the other two are wrong: the second answer starts well by computing the rounded income, but it makes no sense to subtract a percentage from a value. Computing the 15% of something means to consider a fraction of that something, not subtracting 15 from that number.

The third answer proposes an alternative approach, in theory, but applies it poorly: instead of computing the whole income and then considering its 15%, you may directly consider the 15% of the bottles and say that the income generated by those bottles will go to charity. The mistake lies in the fact that the 15% of about 120 bottles is not 15 bottles (that would have been the case if the bottles were exactly 100).

Answer 2

Find the total he made by multiply the number of bottles sold by the price:

118 x 1.50 = $177

Multiply the total amount made by 15%:

177 x 0.15 = $26.55 ( amount given to charity).

The correct solution would be A.