A toy rocket is lying on its side, ready to be raised into position on its launch pad in the middle of Tappan Square. Stage C (the top stage of the three stages) is 22 cm long. Stage B is as long as Stage C plus 1/2 of stage A. Stage A is as long as stage B and stage C together. How tall is the whole rocket?
We know: C = 22, B = C + A/2, and A = B + C
Then B = C + A/2 = 22 + A/2
And A = B + C so B = A – C = A – 22
And A = B + C so B = A – C = A – 22
We equate the above two expressions for B to get:
22 + A/2 = A – 22
So A/2 = 44
And A = 88
Substituting values for A and C into B = A – C, we get:
B = 88 – 22 = 66
So A + B + C = 88 + 66 + 22 = 176 cm (almost 6 feet tall).