SOLUTION: [ A boy observed that twice his age is 5 more years than his older sister's. His sister observed that twice the square of her brother's age subtracted from the square of her age is

Question 825132: [ A boy observed that twice his age is 5 more years than his older sister's. His sister observed that twice the square of her brother's age subtracted from the square of her age is 7 years. Find the difference in their ages. ]
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = boy
y = girl
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2x = y + 5
yy - 2xx = 7
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y = 2x - 5
yy - 2xx = 7
(2x - 5)(2x - 5) - 2xx = 7
4xx - 20x + 25 - 2xx = 7
2xx - 20x + 18 = 0
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the above quadratic equation is in standard form, with a=2, b=-20, and c=18
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -20 18
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
this quadratic has two real roots (the x-intercepts), which are:
x = 9
x = 1
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NOTE:
y = 2x - 5
for root x=1
y = 2(1) - 5
y = -3
y (the girl's age) cannot be negative:
the root x=1 does not fit this problem statement, so use the root x=9
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solution:
x = boy = 9
y = girl = 13
---
age difference: 4
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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