A father's present age is three years more than three times his son's age.
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A father's present age is three years more than three times his son's age. After three years, the father's age will be ten years more than twice the son's age. What is the father's present age?
Show answer & explanation
By setting up a system of linear equations based on the present and future age relationships, we can solve for the son's age and then use it to find the father's present age.
Step-by-step Derivation:
Step 1: Define variables. Let F be the father's present age and S be the son's present age.
Step 2: Translate the first condition: 'Father's present age is three years more than three times his son's age'.
Equation 1: F = 3S + 3
Step 3: Translate the second condition: 'After three years, the father's age will be ten years more than twice the son's age'.
Father's age in 3 years = F + 3
Son's age in 3 years = S + 3
Equation 2: F + 3 = 2(S + 3) + 10
Step 4: Simplify Equation 2:
F + 3 = 2S + 6 + 10
F + 3 = 2S + 16
F = 2S + 13
Step 5: Set the two expressions for F equal to each other:
3S + 3 = 2S + 13
Step 6: Solve for S:
3S - 2S = 13 - 3
S = 10
Step 7: Substitute S = 10 back into Equation 1 to find F:
F = 3(10) + 3
F = 30 + 3
F = 33
Step 8: Verify with Equation 2: 33 + 3 = 36; 2(10 + 3) + 10 = 2(13) + 10 = 26 + 10 = 36. The values are consistent.