Use x, y, w, and z to clear up the confusion of RpTp and RcTc.

x = Rp

y = Tp

w = Rc

z = Tc

Therefore, you now need to solve for y and w.

xy = 288

wz = 108

x = 3w

y + z = 12

xy = 288

y = 288/x ← divided each side by x

wz = 108

z = 108/w ← divided each side by w

If y + z = 12, then

288/x + 108/w = 12 ← substituted for y and z

288w + 108x = 12xw ← multiplied each side by xw

288w + 108(3w) = 12w(3w) ← substituted 3w for x

288w + 324w = 36w² ← multiplied

612w = 36w² ← combined like terms

36w² - 612w = 0 ← subtracted 612w from each side

36w(w - 17) = 0 ← factored 36w out

36w = 0 or w - 17 = 0 ← set each factor equal to zero

w = 0 or w = 17 ← solved for w

w = 17 only....w = 0 will not work later on

wz = 108 ← equation from above

17z = 108 ← substituted 17 for w

z = 6.353 ← divided by 17

y + z = 12 ← equation from above

y + 6.353 = 12 ← substituted 6.353 for z

y = 5.647 ← subtracted 6.353 from each side

w = 17 and y = 5.647

**Rc = 17 and Tp = 5.647
**

- Proof

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