Problem

3. (a) A father is 28 years older than the son. In 5 years the father's age will be 7 years more than twice that of the son. Find their present age.

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{\text{The father's present age is 44 years old, and the son's present age is 16 years old.}}\)

Steps

Step 1 :Let the father's age be F and the son's age be S. We have two equations:

Step 2 :\(F = S + 28\)

Step 3 :\(F + 5 = 2(S + 5) + 7\)

Step 4 :Solve the system of equations:

Step 5 :Substitute the first equation into the second equation:

Step 6 :\((S + 28) + 5 = 2(S + 5) + 7\)

Step 7 :Simplify the equation:

Step 8 :\(S + 33 = 2S + 17\)

Step 9 :Isolate S:

Step 10 :\(S = 16\)

Step 11 :Substitute the value of S back into the first equation:

Step 12 :\(F = 16 + 28\)

Step 13 :\(F = 44\)

Step 14 :\(\boxed{\text{The father's present age is 44 years old, and the son's present age is 16 years old.}}\)

link_gpt