Richard and Teo have a combined age of 35. Richard is 8 years older than twice Teo's age. How old are Richard and Teo?
Step 1: Convert the words to math. The question is giving us two equations that compare Richard (R) and Teo's (T) ages. The first part of the question says that Richard (R) and Teo (T) have a combined (+) age of (=) 35. The second part of the question says that Richard (R) is (=) 8 years older (+) than twice (2 x) Teo's (T) age. So, now that we translated the English into math, lets assemble the two equations.
R + T = 35
R = 8 + (2 x T)
Step 2: Simplify the second equation. One of the easiest ways to find the values of Richard and Teo's ages are by canceling out one of the variables so that we only have to work with the other variable. To do this we need to to take the second equation and get R and T on the left side of the equal sign.
R = 8 + (2 x T)
Multiply the (2 x T)
R = 8 + 2T
Subtract 2T to the left side
R = 8 + 2T
-2T -2T
R - 2T = 8
Step 3: Cancel one of the variables. If you stack the two equations on top of each other, you can see that R is pretty easy to get rid of if you subtract the two equations
R + T = 35
- R - 2T = 8
3T = 27
Now isolate the T
3T = 27
3 3
T = 9
Step 3: Solve for R. We know that T = 9, so lets plug 9 in for T in the first equation
R + 9 = 35
Now get R by itself on the left side of the equal sign
R + 9 = 35
-9 -9
R = 26
So, Richard is 26 and Teo is 9. Problem solved!
Step 4: Do a celebratory happy dance. You did it!
