SOLUTION: Alan is x years old. His mother's age is the square of his age. If Alan's father is two years older than his mother and the sum of all three ages is 80 years, how old is Alan?

Question 926545: Alan is x years old. His mother's age is the square of his age. If Alan's father is two years older than his mother and the sum of all three ages is 80 years, how old is Alan?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = alan age
y = mom age
z = dad age
---
y = xx
z = y + 2
x + y + z = 80
---
z = xx + 2
x + xx + z = 80
---
x + xx + xx + 2 = 80
---
2xx + x - 78 = 0
---
the above quadratic equation is in standard form, with a=2, b=1 and c=-78
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 1 -78
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
x = 6
x = -6.5
---
the negative root doesn't fit the problem statement, so use the positive root:
---
x = 6
y = 6*6
z = 6*6 + 2
---
x = alan age = 6
y = mom age = 36
z = dad age = 38
---
answer:
L = 18 inches
w = 5 inches
---
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Solve quadratic equations, quadratic formula:
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---
Solve systems of linear equations up to 6-equations 6-variables:
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