Grade 4 level arithmetic maths problem that I can't work out

Question

My grade 4 son was given this problem as homework, except I can't even seem to work it out! Any help is appreciated.

Each student in year 4 was asked to bring a paint tin, a paint brush and glue for art. Each student brought at least 1 item.

18 students brought all three items. 4 students forgot only the glue. 1 student brought only the glue. 2 students brought only a paint brush. Altogether there were 25 paint tins, 25 paint brushes and 22 glue bottles.

How many students were there in year 4?

A. 24 B. 25 C. 29 D. 72

Do fourth graders know Venn diagrams? This problem is straightforward enough to just write out each bit of information and count. — Vincent, Jul 27 '14 at 10:04
Yes, fourth graders absolutely should know about Venn diagrams. It's just drawing circles and counting. Basic maths skills. — Graham Kemp, Jul 27 '14 at 10:14

score 3 · Answer 1 · answered Jul 27 '14 at 10:07

3

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Red letters are what we calculate from the given problem.

answered Jul 27 '14 at 10:07

Vikram

5,580

count each number once to get the size of the class – Vikram Jul 27 '14 at 10:11
Thanks that makes a lot of sense! – Ann231 Jul 27 '14 at 10:14
@Ann231, I am glad that it helped you! – Vikram Jul 27 '14 at 10:23

score 0 · Answer 2 · answered Jul 27 '14 at 10:04

18 students brought all three items. 4 students forgot only the glue. 1 student brought only the glue. 2 students brought only a paint brush. Altogether there were 25 paint tins, 25 paint brushes and 22 glue bottles.

Draw a Venn Diagram of three overlapping circles; for Tin, Brush, and Glue. The areas of each circle must total $25$, $25$, and $22$ respectively.

The area where the three all meet $18$. The area where only Tin and Brush meet is $4$, and the area which is only Brush is $2$. That covers three of the four parts of the Brush circle. The last area in the Brush circle is the number of students who bought only Glue and Brush (but not a Tin). All four areas must add up to $25$, so you can fill it in.

The area which is only Glue is $1$. Now work out the last two area by the same reasoning.

Since there are no students outside the circle, add up all the areas to find the size of the class.

Grade 4 level arithmetic maths problem that I can't work out

2 Answers2