algebra II

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algebra II

RpTp=288

RcTc=108

Rp=3Rc

Tp+Tc=12

Please find Rc and Tp
Proof Proof
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Re: algebra II

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