Answer:
E. 62
Step-by-step explanation:
If we let r, g, b represent the numbers of red, green, and blue disks, respectively, we are given the following relations:
r + g + b = 105 . . . . there are 105 disks, total
r -g = 30 . . . . . . . . . there are 30 more reds than greens
g -b = 21 . . . . . . . . . there are 21 more greens than blues
We can use the third equation to substitute for b in the first equation.
b = g -21 . . . . . third equation solved for b
r + g + (g -21) = 105 . . . . substituted into the first equation
r +2g = 126 . . . . . . . . . . . add 21 and simplify
Now, we can use the second equation to substitute for g in the one we have just written.
g = r -30 . . . . . . second equation solved for g
r +2(r -30) = 126 . . . . . . substituted into our equation for r and g
3r = 186 . . . . . . . . . . . . . simplify and add 60
r = 62 . . . . . . . . . divide by 3
Senja has 62 red disks.
__
<em>Additional comment</em>
g = 62 -30 = 32
b = 32 -21 = 11
Senja has 11 blue and 32 green disks, as well.
