Answer:
The present age of Robie's father is 40 and the present age of Robie is 10.
Step-by-step explanation:
If Robie's father is 4 times as old as Robie and after 5 years he will be 3 times as old as Robie, we have to write this in expression form to further solve. Try putting the father as f and Robie as r. So if f is 4 times r and after 5 years f is 3 time r, then add the first side with f is 4 times r and since 5 years after affects both variables add 5 to both variables in the second side as r becomes a third of f. Written in expression, we have [tex]f=4r; r+5=\frac13(f+5)[/tex]. Having this we can solve by substitution.
To solve by substitution, rewrite the equation (if necessary), substitute the values for variables, and give the answer.
Let us start solving by:
(1) Rewriting the equation (it is necessary right now)
[tex]f=4r; r+5=\frac13(f+5) \\ f=4r; r+5=\frac13f + \frac{5}{3} [/tex]
(2) Substitute the values for variables
(2a) Substitute for f
[tex]f = 4r \\ r + 5 = \frac{1}3f + \frac53 \\ r + 5 = \frac{1}34r + \frac53 \\ r + 5 = \frac{4}3r + \frac53 \\ r + 5 + \frac{ - 4}{3} = \frac{4}3r + \frac53 + \frac{ - 4}{3} \\ \frac{ - 1}{3} r + 5 = \frac{5}{3} \\ \frac{ - 1}{3}r + 5 - 5 = \frac53 - 5 \\ \frac{ - 1}{3} r = \frac{ - 10}{3} \\ \frac{ \frac{ - 1}{3} r}{ \frac{ - 1}{3} } = \frac{ \frac{ - 10}{3} }{ \frac{ - 1}{3} } \\ r = 10[/tex]
(2b) Subsitute for r
[tex]r = 10 \\ f = 4r \\ f = (4)(10) \\ f = 40[/tex]
(3) Give the answer
f (The present age of the father) is 40 and r (the present age of Robie) is 10.
