# Some middle school questions

#### Areecea

##### New member
I'm not sure if these are actually true counting/probability ones, it's just I don't understand them.

1. Kim has red, blue, grey, orange, yellow, and white paints. If she picks 3 in a painting but never uses red and blue together, how many combinations can she have?
2. Professor Stashe awarded 500 certificates, for math and science. Girls won 2/3 of the math and 1/2 of the science certificates. If the number of girls who won for math was 50 more than 3/2 the number of girls who won for science, how many girls won for math?
3. The sequence 72, 75, 76, 81, 84, 85... in which each number is 9 more than the number 3 numbers before it, includes (694, 733, 812, 950)
If you could please explain these to me as I don't get them, I would be eternally grateful! Thanks so much!

#### Subhotosh Khan

##### Super Moderator
Staff member
I'm not sure if these are actually true counting/probability ones, it's just I don't understand them.

1. Kim has red, blue, grey, orange, yellow, and white paints. If she picks 3 in a painting but never uses red and blue together, how many combinations can she have?
2. Professor Stashe awarded 500 certificates, for math and science. Girls won 2/3 of the math and 1/2 of the science certificates. If the number of girls who won for math was 50 more than 3/2 the number of girls who won for science, how many girls won for math?
3. The sequence 72, 75, 76, 81, 84, 85... in which each number is 9 more than the number 3 numbers before it, includes (694, 733, 812, 950)
If you could please explain these to me as I don't get them, I would be eternally grateful! Thanks so much!
Kim has red, blue, grey, orange, yellow, and white paints. If she picks 3 in a painting but never uses red and blue together, how many combinations can she have?

Suppose there was no restriction - and she could choose any 3 colors she wanted then - how many combinations can she have?

The sequence 72, 75, 76, 81, 84, 85... in which each number is 9 more than the number 3 numbers before it, includes (694, 733, 812, 950)

This is NOT asking for anything?

#### stapel

##### Super Moderator
Staff member
[*]Professor Stashe awarded 500 certificates, for math and science. Girls won 2/3 of the math and 1/2 of the science certificates. If the number of girls who won for math was 50 more than 3/2 the number of girls who won for science, how many girls won for math?
i) Pick variables for each of the certificates; say, "m" for "math" and "s" for "science".
ii) What expression stands for the number of math certificates that the girls won?
iii) What expression stands for the number of science certificates that the girls won?
iv) What expression stands for "3/2 the number of girls who won for science"?
v) What expression stands for "50 more than" the previous amount?
vi) What equation stands for "the number of girls who won for math was" equal to the above amount?
vii) Given that there were 500 certificates in total, what expression stands for the number of science certificates, in terms of the certificates left after awarding the math certificates?
viii) Substituting the expression from (vii) into the equation in (vi), what equation results?
ix) The equation in (viii) should be in terms only of the variable "m". Solve for the value of "m".
x) Back-solve for the number of girls who won math certificates.