''Two years ago john was 5 times older than Bill.......

eddy2017

eddy2017

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Joined
Oct 27, 2017
Messages
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how about this one?. a little bit more complex, but nothing that can not be solved.
let's see if i hit the proverbial nail right on its fat head.

''Two years ago john was 5 times older than Bill. He is 8 years older than him now. How old is John?''
this time i am going to assign variables.
John’s age =x
Bill’s age= y
John’s age now
X=y+8 ( now he is 8 years older than Bill)
Now, let’s try to visualize what was going on two years ago.
John(x) was two years younger two yrs ago x-2
Bill (y) was two years younger two yrs ago. Y-2
Two years ago john was 5 times older than Bill.
John-2 =Bill*5
Joh is 8 years older than Bill now. So,
John +8 = Bill+2 (the ‘2’ for the two years ago)
Now, we can set up two equations from what we have above
A) x-2 =5y
B) x -8 =y+2 John is 8 yrs older now
Let’s solve for x in equation B
x-8=Y+2
x-8 + 8 = Y + 2 -8
x=y+2+8
We have the value of x
Let’s sub x in equation A
A) x-2 =5y
Y+8+2-2=5y
Y+8=5Y
-y + y + 8 =5Y-y
8=4Y
Y=8/4
y=2
Now let’s replace y in equation x=y+2+8
X=2+2+4
X=12
So, john’s current age is 12 years old

I'll switch topics now. this is getting a little bit tiresome. lol
 
eddy2017 said:
''Two years ago john was 5 times older than Bill. He is 8 years older than him now. How old is John?''
Click to expand...
You're aware, I hope, that you can (and should) check your answer by putting it into the story:
eddy2017 said:
John’s age =x
Bill’s age= y
Click to expand...
eddy2017 said:
y=2
X=12
So, john’s current age is 12 years old
Click to expand...
So here's the check:

John is 12, and Bill is 2. Two years ago John was [10, which is] 5 times older than Bill (who was then ... 0?]. He [John, 12] is 8 years older than him [Bill, 2] now.​

But 10 is not 5 times 0, and 12 is not 8 more than 2. So something seems to be wrong. Can you see where it is?

In another thread you made a table to keep track of the different ages, which is just what I would do. That might have helped here.
 
Dr.Peterson said:
You're aware, I hope, that you can (and should) check your answer by putting it into the story:


So here's the check:

John is 12, and Bill is 2. Two years ago John was [10, which is] 5 times older than Bill (who was then ... 0?]. He [John, 12] is 8 years older than him [Bill, 2] now.​

But 10 is not 5 times 0, and 12 is not 8 more than 2. So something seems to be wrong. Can you see where it is?

In another thread you made a table to keep track of the different ages, which is just what I would do. That might have helped here.
Click to expand...
Right. Let me check it. Yes, the table helps a lot. I just wanted to try with the variables but it is a bit more tricky
 
eddy2017 said:
how about this one?. a little bit more complex, but nothing that can not be solved.
let's see if i hit the proverbial nail right on its fat head.

''Two years ago john was 5 times older than Bill. He is 8 years older than him now. How old is John?''
this time i am going to assign variables.
John’s age =x
Bill’s age= y
John’s age now
X=y+8 ( now he is 8 years older than Bill)
Now, let’s try to visualize what was going on two years ago.
John(x) was two years younger two yrs ago x-2
Bill (y) was two years younger two yrs ago. Y-2
Two years ago john was 5 times older than Bill.
John-2 =Bill*5
Joh is 8 years older than Bill now. So,
John +8 = Bill+2 (the ‘2’ for the two years ago)
Now, we can set up two equations from what we have above
A) x-2 =5y
B) x -8 =y+2 John is 8 yrs older now
Let’s solve for x in equation B
x-8=Y+2
x-8 + 8 = Y + 2 -8
x=y+2+8
We have the value of x
Let’s sub x in equation A
A) x-2 =5y
Y+8+2-2=5y
Y+8=5Y
-y + y + 8 =5Y-y
8=4Y
Y=8/4
y=2
Now let’s replace y in equation x=y+2+8
X=2+2+4
X=12
So, john’s current age is 12 years old

I'll switch topics now. this is getting a little bit tiresome.
Click to expand...
I do not think that saying John’s age =x and Bill’s age= y is very clear. You should say, for clarity, that
John’s age now =x and Bill’s age now = y.

I would have used J for John's age now and B for Bill's age now so i would not have to keep looking back to see what x and y equals. BTW, you used X and Y in your work but never defined them!

Two years ago john was 5 times older than Bill.
John-2 =Bill*5
When you are told that two years ago John was 5 times older than Bill, does this mean that two years ago John was times older than Bill is today or does it mean that two years ago John was times older than Bill was two years ago?
 
eddy2017 said:
Right. Let me check it. Yes, the table helps a lot. I just wanted to try with the variables but it is a bit more tricky
Click to expand...
It's still variables when you make a table; the table just helps you keep track of which expression has which meaning.

And have you looked for the error? It involves mere inconsistency in the meaning of y.
 
Dr.Peterson said:
It's still variables when you make a table; the table just helps you keep track of which expression has which meaning.

And have you looked for the error? It involves mere inconsistency in the meaning of y.
Click to expand...
let's make a table. I am confused now. let me try something first and then i wanna see the table. somehow i went wrong in my calculations in the original answer. I'll post my work now.
 
John's age NOW=x
Bill's age NOW =y

Two years ago x-2= 5(y-2)
now x-8=y

i will try to solve this as a system of equations
x-2= 5(y-2)
x-8=y

x-2= 5(x-8-2)
x-2=5(x-10)
x-2=5*x -50
Let's solve your equation step-by-step.
x−2=5x−50
Step 1: Subtract 5x from both sides.
x−2−5x=5x−50−5x
−4x−2=−50
Step 2: Add 2 to both sides.
−4x−2+2=−50+2
−4x=−48
Step 3: Divide both sides by -4.
−4x/-4 =−48/-4
x=12
john is 12 yrs

then if x=12
x-8=y
12-8=4

Bill is 4

john is 12 years old. Bill's senior by 8 years
 
Last edited:
if you confirm this way, i would try and solve it drawing a table and post it or ask if in doubt
 
eddy2017 said:
John's age NOW=x
Bill's age NOW =y

Two years ago x-2= 5(y-2)
now x-8=y

i will try to solve this as a system of equations
x-2= 5(y-2)
x-8=y

x-2= 5(x-8-2)
x-2=5(x-10)
x-2=5*x -50
Let's solve your equation step-by-step.
x−2=5x−50
Step 1: Subtract 5x from both sides.
x−2−5x=5x−50−5x
−4x−2=−50
Step 2: Add 2 to both sides.
−4x−2+2=−50+2
−4x=−48
Step 3: Divide both sides by -4.
−4x/-4 =−48/-4
x=12
john is 12 yrs

then if x=12
x-8=y
12-8=4

Bill is 4

john is is senior in 8 years
Click to expand...
eddy2017 said:
John's age NOW=x
Bill's age NOW =y

Two years ago x-2= 5(y-2)
now x-8=y

i will try to solve this as a system of equations
x-2= 5(y-2)
x-8=y

x-2= 5(x-8-2)
x-2=5(x-10)
x-2=5*x -50
Let's solve your equation step-by-step.
x−2=5x−50
Step 1: Subtract 5x from both sides.
x−2−5x=5x−50−5x
−4x−2=−50
Step 2: Add 2 to both sides.
−4x−2+2=−50+2
−4x=−48
Step 3: Divide both sides by -4.
−4x/-4 =−48/-4
x=12
john is 12 yrs

then if x=12
x-8=y
12-8=4

Bill is 4

john is is senior in 8 years
Click to expand...
You were asked to find John's age. Have you stated his age?
 
eddy2017 said:
I did
Click to expand...
Good. My point is that one can do all good work but fail to answer the question. For example, if they asked how old John would be in 4 years, then all your work would be fine. You'd just have to now answer the question--in 4 years John would be 16 years old.
 
I want to give the table method a try again. If you all don't mind. I was comparing it to the one I posted but I'm afraid is not the same. It will have to be tweaked . I'll take a break now.
You all have a good evening wherever you are. And thank you. Forgive me for my stupidity. I do love you all!
 
My $0.02 worth : 2 years ago John was 5 times older than Bill, and, just like today, he was 8 years older. Thought it might simplify the problem a little bit.
 
eddy2017 said:
John's age NOW=x
Bill's age NOW =y

Two years ago x-2= 5(y-2)
now x-8=y

i will try to solve this as a system of equations
x-2= 5(y-2)
x-8=y

x-2= 5(x-8-2)
x-2=5(x-10)
x-2=5*x -50
Let's solve your equation step-by-step.
x−2=5x−50
Step 1: Subtract 5x from both sides.
x−2−5x=5x−50−5x
−4x−2=−50
Step 2: Add 2 to both sides.
−4x−2+2=−50+2
−4x=−48
Step 3: Divide both sides by -4.
−4x/-4 =−48/-4
x=12
john is 12 yrs

then if x=12
x-8=y
12-8=4

Bill is 4

john is 12 years old. Bill's senior by 8 years
Click to expand...
Yes, your work and your answer are correct.

eddy2017 said:
I want to give the table method a try again. If you all don't mind. I was comparing it to the one I posted but I'm afraid is not the same. It will have to be tweaked . I'll take a break now.
Click to expand...
The table will not change the work at all; it is just a way to make sure you keep track of the meaning of each expression, so that your equations are correct, and so that you interpret the answer correctly.
 
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