Question

6. *Five classmates came to Dan's birthday party. This is half as many as the numberof friends from his summer camp, and one third as many as the number of hisrelatives that were there. How many people were at Dan's birthday party, if relatives,friends from the summer camp, and classmates are all different people?

Answer 1

Let's use the letters:

• C for the number of classmates at the party,

,

• S for the number of friends from summer camp at the party,

,

• R for the number of relatives at the party.

So, the total number of people at the party is:

C + S + R

We ere already informed that the number of classmates is 5. So:

C = 5

Also, we know that 5 is half as many as the number of friends from his summer camp. So:

5 = S/2

Multiplying both sides of the relation above, we find:

2 * 5 = 2 * S/2

10 = S

S = 10

Now, we also know that 5 is one-third as many as the number of his relatives that were there. So, we have:

5 = R/3

3 * 5 = 3 * R/3

15 = R

R = 15

Therefore, the total number of people at the party is:

C + S + R = 5 + 10 + 15 = 30

Answer: There were 30 people at Dan's birthday party.