SOLUTION: RaTa= 160, RbTb= 240, Rb=2Ra, Ta+Tb=7 Solve? I'm not sure how to do this... help? Thanks!!

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Question 146507: RaTa= 160, RbTb= 240, Rb=2Ra, Ta+Tb=7
Solve? I'm not sure how to do this... help? Thanks!!
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
R%5Ba%5D%2AT%5Ba%5D=+160 Start with the first equation


R%5Ba%5D=+160%2FT%5Ba%5D Solve for R%5Ba%5D


T%5Ba%5D%2BT%5Bb%5D=7 Move onto the last equation


T%5Bb%5D=7-T%5Ba%5D Solve for T%5Bb%5D



R%5Bb%5D%2AT%5Bb%5D=+240 Now move onto the second equation


%282%2AR%5Ba%5D%29%2AT%5Bb%5D=+240 Plug in R%5Bb%5D=+2%2AR%5Ba%5D


%282%2A%28160%2FT%5Ba%5D%29%29%2AT%5Bb%5D=+240 Plug in R%5Ba%5D=+160%2FT%5Ba%5D


%28320%2FT%5Ba%5D%29%2AT%5Bb%5D=+240 Multiply and simplify


%28320%2FT%5Ba%5D%29%2A%287-T%5Ba%5D%29=+240 Plug in T%5Bb%5D=7-T%5Ba%5D


2240%2FT%5Ba%5D-320=+240 Distribute


2240-320T%5Ba%5D=+240T%5Ba%5D Multiply every term by the LCD T%5Ba%5D


2240=+240T%5Ba%5D%2B320T%5Ba%5D Add 320T%5Ba%5D to both sides


2240=+560T%5Ba%5D Combine like terms


4=+T%5Ba%5D Divide both sides by 560 to isolate T%5Ba%5D. So the first answer is T%5Ba%5D=4



T%5Ba%5D%2BT%5Bb%5D=7 Go back to the last equation


4%2BT%5Bb%5D=7 Plug in T%5Ba%5D=4


T%5Bb%5D=3 Solve for T%5Bb%5D


From here it's not too difficult to find R%5Ba%5D and R%5Bb%5D. So I'll let you finish.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
substituting __ (2Ra)Tb=240 __ dividing by 2 __ RaTb=120

adding __ RaTa+RaTb=160+120 __ factoring __ Ra(Ta+Tb)=280

substituting __ Ra(7)=280 __ dividing by 7 __ Ra=40

substituting __ (40)Ta=160 __ dividing by 40 __ Ta=4

substituting __ (4)+Tb=7 __ subtracting 4 __ Tb=3

substituting __ Rb=2(40) __ Rb=80