Algebra Problem! Please Help!

Question

Solve for unknowns: R_AT_A = 360; R_BT_B = 60; R_A = 3R_B; T_A+T_B = 12

Then evaluate: R_A - R_B + T_A - T_B =

Answer 1

RA*TA=360

RB*TB=60

RA=3RB

TA+TB=12

3RB*(12-TB)=360

3RB(12-60/RB)=360

36RB-180=360

36RB=540

RB=15

so RA=45

45TA=360

TA=8

so TB=4

45-15+8-4=34

Answer 2

You have 4 unknowns, and you are given 4 equations. Since there are 4 unique equations, there is enough information to solve the problem

R_AT_A = 360

R_BT_B = 60

R_A = 3R_B

T_A+T_B = 12

The 3rd equation relates RA and RB. We can start by finding another equation with the same variables. The 1st 2 equations allow us to relate the "T" variables to the "R" variables:

TA = 360/RA

TB = 60/RB

Next, substitute into equation 4 to get:

360/RA + 60/RB = 12

Now, we have 2 equations with RA and RB. Solve using substitution to get RA and RB.

Once you have RA and RB, use the the first 2 equations to get TA and TB.