Problem of the Week
Problem A and Solution
Tasty Tarts

Problem

Genevieve and Dima decided to make peach tarts. According to their recipe, each tart requires three-quarters of a peach. If they bought a dozen peaches, how many tarts can they make?

Solution

Here is one way to solve the problem. We can draw a diagram of a dozen peaches where each peach is divided into four quarters. Then we group three quarters together with a common label, corresponding to the tart that those quarters are used in. We continue to identify groups of three quarters over the dozen peaches. Finally, we count the number of groups we have identified.

First peach: 1,1,1,2

Second peach: 2,2,3,3

Third peach: 3,4,4,4

Fourth peach: 5,5,5,6

Fifth peach: 6,6,7,7

Sixth peach: 7,8,8,8

Seventh peach: 9,9,9,10

Eighth peach: 10,10,11,11

Ninth peach: 11,12,12,12

Tenth peach: 13,13,13,14

Eleventh peach: 14,14,15,15

Twelfth peach: 15,16,16,16

From this diagram, we can see that Genevieve and Dima can make \(16\) tarts with a dozen peaches.