Draw Venn diagram for this situation This year 120 students receive gold star, 180 students receive certificates and 80 students receive blue ribbon. Of these, 40 students receive gold star with no other award, 50 students receive certificates with no other reward and 10 students receive blue ribbons with no other rewards. In addition, 10 students receive all awards and 65 students receive no awards. Draw the Venn diagram to represent this situation and determine how many students attend the schools this year.

Here is my Venn diagram:

![enter image description here](

I let $a$ be the number of Gold and Ribbon.

In doing so I worked out there must be $(70-a)$ Gold and Cert and $(60-a)$ Ribbon and Cert.

I solved the equation $70-a+60-a+10+50=180$ to get $a=5$

Does this help?