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Correction: Bob is thrice as old as Peter. Let b be the current age of Bob, and p the current age of Peter. Now, b=3p Six years earlier the relations was: b-6=4*(p-6)=4p-24. Take the 6 to the right side leaving b=4p-18 Remember that now b=3p. Use it in the equation above b=(3p)=4p-18, This becomes 3p=4p-18 or 0=p-18, and p=18 Peter is 18 years old, and Bob is 3*18=54 years old. Verification: 6 years ago Peter was 12 years old and Bob 48 years old. 48/12=4.
So the father is 3 times as old as his daughter. Let F represent the age of the fatherLet D represet the age of the daughter So we know from the first sentence, F = 3 * D From the second sentence, 12 years from now the father is 1 year les than twice his daughters age, First, lets assume it's not 12 years from now (to avoid confusion), we would haveF + 1= 2 * D But since its 12 years from now, we have to add 12 to both ages (F + 12) + 1 = 2 * (D + 12) Let's simplify a bit,
F + 13 = 2 * D + 24F = 2D + 11 Now we have to solve these two equations together, we can plug the first equation into the second, F = 3 * DF = 2 * D + 11 3 * D = 2 * D + 11D = 11 So the daughter is 11 years old, we can find out how old the father is by plugging into the first equation F = 3 * DF = 3 * 11F = 33 So the father is 33 and the daughter is 11.
First we have 2 variables, their ages: I used Allan = x & Roy = y
Equation 1: X - 4 = 2*(Y-4) - 3
We can ignore the 5 years in the second part of the statement. Allan will always be 6 years older than Roy whether it be 5 years from now or ten years form now.
Equation 2: X = Y + 6
Substitute Y + 6 for X in equation 1:
X - 4 = 2*(Y-4) - 3 becomes Y + 6 - 4 = 2*(Y-4) - 3
That simplifies to Y + 2 = 2Y - 8 - 3
Rewrite it again: Y + 2 = 2Y - 11
Add 11 to both sides: Y + 13 = 2Y
Subtract Y from both sides: 13 = Y
Now plug 13 in for y in Equation 2
X = Y + 6
X = 13 + 6
X = 19