algebra II

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algebra II

 RpTp=288 RcTc=108 Rp=3Rc Tp+Tc=12 Please find Rc and Tp
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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