Question

ACT math practice question.
There are three colors of jelly beans in a bowl. If there are 5 more red ones than blue, and there are 9 more blue ones than green, and the total number of beans is 26, how many green ones are in the bowl?

Now I know there should be some equation set up that I can then solve, I just can't think of what the equation would be for some reason. Please help!

Answer 1

Let the number of red balls be r, the number of blue balls be b and the number of green balls be g. Try set up a set of equations.

Answer 2

All I got is
b + 5 = r
and
b - 9 = g

But I don't know how that is solvable. Not enough information.

Answer 3

how many total jelly beans?

Answer 4

26

Answer 5

what would be the equation for that total?

Answer 6

in terms of the variables...

Answer 7

b + r + g = 26.
But I have a feeling that's not it...
Would (b + 5) + (b - 9) + b = 26 work?
Even then I don't know how that is solvable either.

Answer 8

yes, and yes...

to solve the last eq you wrote, comine like terms, isolate the variable and voila!

Answer 9

"combine"

Answer 10

Oh! Okay, I think it is coming back to me. It's just been a while since I've done this.
So to combine like terms, before simplifying it, would I get
2b - 9b + 5b -45 + b = 26 ??

Answer 11

Oh wait, that can't be it because I just got that b = -26 ...

Answer 12

not quite...

(b+5)+b+(b-9) = 29 =>b+b+b+5-9=26 => 3b - 4 = 26

can you solve from there?

Answer 13

26 not 29

Answer 14

Okay, thanks I can!

Answer 15

what do you get? for r, b and g?

Answer 16

\[green=x\]\[blue=x+9\]\[red=(x+9)+5=x+14\]\[g+b+r=x+x+9+x+14=3x+23\]\[3x+23=26\]\[x=1\]

Answer 17

\[green=x=1\]\[blue=x+9=1+9=10\]\[red=x+14=1+14=15\]\[1+10+15=26\]
as given

Answer 18

r