There are 33 students in the band there six more 5th grade students than 3rd grade students there is an equal number of third grade and fourth grade students how many 3rd grade students are in the band

Use A for third graders, B for fourth graders, and C for fifth graders.

33 = A + B + C

Since there are three variables, you need to come up with two other equations to substitute in.

C = 6 + A Since there are six more fifth graders than third graders.

A = B Since there is an equal amount of third and fourth graders.

Since A is in both equations, lets put each variable in terms of A.

B = A

C = 6 + A

So:

A+A+A+6=33

A+A+A=27 Since you subtract six from both sides.

3A=27 Since you combine all three A's.

A=9 Since you divide both sides by three.

Therefore, since A is the number of third graders, there are 9 third graders.

Linda · 7 years ago

   Bob B

   Use T for third graders, F for fourth graders and X for fifth graders and write what you know as equations:

   T + F + X = 33 [There are 33 students in the band.]

   X = T + 6 [6 more 5th graders than 3rd graders.]

   T = F [Equal # of 3rd & 4th graders]

   Since T equals F and X equals T + 6, substitute those into the first equation:

   T + T + (T + 6) = 33

   Combine into:

   3T + 6 = 33

   Subtract 6 from both sides:

   3T = 27

   Divide both sides by 3:

   T = 9

   There are 9 third graders.

9 3rd graders

Step-by-step explanation:

9 3rd

14 5th

9 4th

9+9+14=33