Question 630681: Can you please help,Von is thrice as old as his brother Jon. Four years ago, he was 4 years less than 5 times Jon�s age at that time. How old are they now?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! v = von's age
j = jon's age.
v = 3j is your first equation.
v-4 = 5(j-4)-4 is your second equation.
you have 2 equations that need to be solved simultaneously.
they are:
v = 3j
v-4 = 5(j-4)-4
simplify the second equation to get:
v-4 = 5j-20-4 which simplifies further to:
v-4 = 5j-24
add 4 to both sides of this equation to get:
v = 5j-20
your 2 equations are now:
v = 3j
v = 5j-20
since both expressions on the right side of each equation are equal to v, you can set these expressions equal to each other to get:
3j = 5j-20
subtract 5j from both sides of this equation to get:
-2s = -20
divide both sides of this equation by -2 to get:
j = 10
your first equation was:
v = 3j
this makes v = 30
your second equation was:
v-4 = 5(j-4)-4
replace v with 30 and j with 10 to get:
30-4 = 5(10-4)-4 which simplifies to:
26 = 50-20-4 which simplifies further to:
26 = 30-4 which simplifies further to:
26 = 26
the values of 30 for v and 10 for j are good.
Answer by ikleyn(52921)  (Show Source):
You can put this solution on YOUR website! .
Can you please help,
Von is thrice as old as his brother Jon. Four years ago, he was 4 years less than 5 times Jon's age at that time.
How old are they now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This problem can be solved in hard way, using two equations and writing many words, as tutor @Theo did in his post.
It also can be solved in easier way, using one equation and writing only the necessary words, as I present it below.
Let x be the Jon age.
Then the Von age is 3x, according to the problem.
Four years ago, the Jon's age was x-4.
Four years ago, the Von's age was (3x-4).
From the problem, we have this equation
3x-4 = 5(x-4) - 4. (Four years ago, Von was 4 years less than 5 times Jon's age at that time).
It is an equation to solve. Simplify and find x
3x - 4 = 5x - 20 - 4.
Collect the terms with 'x' on the right side; collect the constant terms on the left side
-4 + 20 + 4 = 5x - 3x,
20 = 2x
x = 20/2 = 10.
Thus, Jon is 10 years old; Von is 3*10 = 30 years old. <<<---=== ANSWER
Solved. The solution is clear, transparent and straightforward, with no excessive words that only distract attention.
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