Explanation:
Hey! This can be represented in a system of linear equations
- f - 8 = 6(s - 8)
- f + 12 = 2(s + 12)
Where,
f = Mr. Fontana's Age
s = Son's Age
Step 1: Solve equation 1
➟ f - 8 = 6(s - 8)
Expanding 6(s - 8)
➟ f - 8 = 6s - 48
Add 8 to both sides
➟ f - 6s = - 48 + 8
➟ f - 6s = - 40 ( This is our first linear equation )
Step 2: Solve equation 2
➟ f + 12 = 2(s + 12)
Expanding 2(s + 12)
➟ f + 12 = 2s + 24
Subtract 12 from both sides
➟ f - 2s = 24 - 12
➟ f - 2s = 12 ( This is our second linear equation )
Now we can find the father's age (f) and his son's age (s). First, multiply the second equation by -1, giving us: -f + 2s = - 12
➟ 12 + 2s - 6s = - 40
➟ 12 - 4s = - 40
➟ - 4s = - 40 - 12
➟ - 4s = - 52
➟ s = - 52 / - 4
➟ s = 13
Mr. Fontana's age (f), now that we know his son’s age (s):
Step 3: Substitute s = 13 into one of the original equations to find f
Choosing equation 1:
➟ f - 8 = 6(s - 8)
Substitute s with 13:
➟ f - 8 = 6(13 - 8)
➟ f - 8 = 6(5)
➟ f - 8 = 30
Add 8 to both sides:
➟ f = 30 + 8
➟ f = 38
So, Mr. Fontana's age (f) is 38 years old, and his son's age (s) is 13 years old.
To summarize, we have:
Mr. Fontana's Age (f) = 38 years old
Son's Age (s) = 13 years old