SOLUTION: Tony is twice as old as Jon. Jon is five years older than Matt. Angie is five years older than half of Jon's age. If the sum of their ages is 180, how old is Jon?

Question 823320: Tony is twice as old as Jon. Jon is five years older than Matt. Angie is five years older than half of Jon's age. If the sum of their ages is 180, how old is Jon?
Found 3 solutions by algebrahouse.com, TimothyLamb, stanbon:
Answer by algebrahouse.com(1659)   (Show Source): You can put this solution on YOUR website!
x = Jon's age
2x = Tony's age {Tony is twice as old as Jon}
x - 5 = Matt's age {Jon is five years older than Matt}
0.5x + 5 = Angie's age {Angie is five years older than half of Jon's age}

x + 2x + x - 5 + 0.5x + 5 = 180 {the sum of their ages is 180}
4.5x = 180 {combined like terms}
x = 40 {divided each side by 4.5}

Jon is 40

For more help from me, visit: www.algebrahouse.com

Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
---
x = tony
y = jon
z = matt
u = angie
---
x = 2y
y = z + 5
u = y/2 + 5
x + y + z + u = 180
---
put the system of linear equations into standard form
---
x - 2y = 0
y - z = 5
0.5y - u = -5
x + y + z + u = 180
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
answer:
x= tony = 80
y= jon = 40
z= matt = 35
u= angie = 25
---
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
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Tony is twice as old as Jon. Jon is five years older than Matt. Angie is five years older than half of Jon's age. If the sum of their ages is 180, how old is Jon?
------
Equations:
t = 2j
j = m + 5
a = (1/2)j+ + 5
t + j + m + a = 180
--------
2j + j + j-5 +(1/2)j+5 = 180
----------------------------------
(9/2)j = 180
(1/2)j = 20
j = 40 yrs (Jon's age now)
-----
t = 2j = 80 (Tony's age now)
-------
m = j-5 = 35 yrs (Matt's age now)
----
a = (1/2)j+5 = 25 yrs (Angie's age now)
=============
Cheers,
Stan H.
=============

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