SOLUTION: the combined ages of two people is 75 years. in 15 years time one person's age will be twice the other person's present age. find their present age?

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Question 880766: the combined ages of two people is 75 years. in 15 years time one person's age will be twice the other person's present age. find their present age?
Answer by Boyen(12) About Me  (Show Source):
You can put this solution on YOUR website!
x = person 1
y = person 2
x+y =75
x+15 = 2y
y = (x+15)/2
x+(x+15)/2 = 75
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=45.
  • Graphical form: Equation x%2B%28x%2B15%29%2F2=75 was fully solved.
  • Text form: x+(x+15)/2=75 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B%28x%2B15%29%2F2=75+%29
    For tutors: simplify_cartoon( x+(x+15)/2=75 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2B%28x%2B15%29%2F2=highlight_red%28+75+%29.
Moved these terms to the left highlight_green%28+-75+%29
It becomes x%2B%28x%2B15%29%2F2-highlight_green%28+75+%29=0.
Look at x%2Bhighlight_red%28+%28x%2B15%29%2F2+%29-75=0.
Expanded term 1%2F2 by using associative property on %28x%2B15%29
It becomes x%2Bhighlight_green%28+1%2F2%2Ax+%29%2Bhighlight_green%28+1%2F2%2A15+%29-75=0.
Look at x%2Bhighlight_red%28+1+%29%2F2%2Ax%2B1%2F2%2A15-75=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2Bx%2F2%2B1%2F2%2A15-75=0.
Look at x%2Bx%2F2%2Bhighlight_red%28+1+%29%2F2%2Ahighlight_red%28+15+%29-75=0.
Multiplied numerator integers
It becomes x%2Bx%2F2%2Bhighlight_green%28+15+%29%2F2-75=0.
Look at x%2Bx%2F2%2Bhighlight_red%28+15%2F2+%29-highlight_red%28+75+%29=0.
Added fractions or integers together
It becomes x%2Bx%2F2-highlight_green%28+135%2F2+%29=0.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+x%2F2+%29-135%2F2=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x%2F2+%29 replacing them with highlight_green%28+%281%2B1%2F2%29%2Ax+%29
It becomes highlight_green%28+%281%2B1%2F2%29%2Ax+%29-135%2F2=0.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1%2F2+%29%29%2Ax-135%2F2=0.
Added fractions or integers together
It becomes %28highlight_green%28+3%2F2+%29%29%2Ax-135%2F2=0.
Look at highlight_red%28+%28highlight_red%28+3%2F2+%29%29%2Ax+%29-135%2F2=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+1%2F2+%29
It becomes highlight_green%28+3+%29%2Fhighlight_green%28+2+%29%2Ax-135%2F2=0.
Look at highlight_red%28+3%2F2%2Ax-135%2F2+%29=0.
Solved linear equation highlight_red%28+3%2F2%2Ax-135%2F2=0+%29 equivalent to 1.5*x-67.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=45.

Universal Simplifier and Solver


Done!


So x=45
x+15 = 2y
so 2y = 60
y=30