John is currently two years older than half of his father's age in years. In 12 years, John will be twothirds his father's age. How many years younger will John be then compared to his father's age now?
x = father's age now
x/2 + 2 = John's age now {John is currently 2 years older than half his father} x + 12 = father's age in 12 years {added 12 onto current age} x/2 + 14 = John's age in 12 years {added 12 onto current age} (x/2) + 14 = (2/3)(x + 12) {in 12 years John will be 2/3 his father's age} 3x + 84 = 4(x + 12) {multiplied entire equation by 6 to eliminate fractions} 3x + 84 = 4x + 48 {used distributive property} x = 36 {subtracted 3x and subtracted 48 from each side} x/2 + 2 = 20 {substituted 36, in for x, into x/2 + 2} John is 20 father is 36  Algebra House Comments are closed.

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