Age Word Problem Involving Ratio

[harpazo]

Homework Statement

Find the present ages of Abraham and Adam.

Relevant Equations

(4x + 4)/(7x + 4) = 3/4

The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.

I never saw an age problem involving a ratio but let's see.

Abraham to Adam = 5 : 7

Let x = present age of Abraham and Adam.

Age of Abraham = 5x.

Age of Adam = 7x.

Age of Abraham to age of Adam =
5x : 7x.

Age of Abraham in 4 years = 4x + 4.

Age of Adam in 4 years = 7x + 4.

Four years from now, the ratio of their ages = 3 : 4.

I got stuck here. A friend said to do the following:

(4x + 4)/(7x + 4) = 3/4

What data in the problem indicates to set up the equation as my friend said? I will then continue to find their ages.

 

[BvU]

What data in the problem

None. In the problem statement it says 5 (five), not 4 (four)

Surely you can solve $$ {5x+4\over 7x+4 } = {3\over 4} \quad ? $$

And:

Let x = present age of Abraham and Adam.

Age of Abraham = 5x.

For the first line, you mean : Let 5x = ...

$\$

 

[FactChecker]

Let x = present age of Abraham and Adam.

There are two ages, one of Abraham and another of Adam. That requires two distinct variables.

EDIT: Probably "requires" is too strong a word. But the two ages are certainly not the same, so x can only represent one age. I recommend that the first translation from words to variables and equations be the most routine and direct translation that you can do. Two variables, one for each person's age, would allow that, no matter what the following word statements are.

 

[harpazo]

There are two ages, one of Abraham and another of Adam. That requires two distinct variables.

Ok.

Let x = Abraham's age

Let y = Adam's age

 

[harpazo]

None. In the problem statement it says 5 (five), not 4 (four)

Surely you can solve $$ {5x+4\over 7x+4 } = {3\over 4} \quad ? $$

And:

For the first line, you mean : Let 5x = ...

$\$

Where did I say I cannot solve the stated equation?

 

[harpazo]

None. In the problem statement it says 5 (five), not 4 (four)

Surely you can solve $$ {5x+4\over 7x+4 } = {3\over 4} \quad ? $$

And:

For the first line, you mean : Let 5x = ...

$\$

What data in the problem indicates to set up the equation as my friend said?

 

[symbolipoint]

Where did I say I cannot solve the stated equation?

Do not get distracted. Keep things in order. You later were able to assign each of two different variables. Best to continue from that. y for Adam and x for Abraham.

 

[Lnewqban]

What data in the problem indicates to set up the equation as my friend said?

The current ages can only be either:
Abraham/Adam: 5/7 or 10/14 or 15/21 or 20/28 or 25/35 or 30/42 or 35/49 or 40/56 or 45/63 or 50/70 or 55/77 or 60/84 or 65/91.
All of the above satisfy the 5/7=0.7143 ratio.

Following the above possible combinations and adding four years to each person, the future ages could be either:
Abraham/Adam: 9/11 or 14/18 or 19/25 or 24/32 or 29/39 or 34/46 or 39/53 or 44/60 or 49/67 or 54/74 or 59/81 or 64/88 or 69/95.
Which ones of the above satisfy the 3/4=0.75 ratio?

 

[symbolipoint]

Rewriting the problem statement and the setup:Homework Statement: The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.

Relevant Equations: (none)

The member has chosen x for Abraham and y for Adam.

First part of the question translates directly as x/y=5/7.

Second part of the question directly translates as (x+4)/(y+4)=3/4.

THOSE are the two equations as a system that can and should be solved.

 

[BvU]

Where did I say I cannot solve the stated equation?

You are right: your post says you can't state the equation to be solved, not the other way around.

The problem statement you posted -- slightly edited

Homework Statement::
The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.

And the

Relevant Equation:: (4x + 4)/(7x + 4) = 3/4

is wrong.

You can't say

Let x = present age of Abraham and Adam.

since they are not equal. And in addition it contradicts the next line -- which in itself is a very good start

Age of Abraham = 5x.

because then from the problem statement it follows that Adam is 7x.

The remainder of the problem statement then tells you that in four years, when their ages are 5x+4 and 7x+4, those have a ratio 3/4. Voila the crucial equation of your friend (who was either mistaken or misquoted). One equation with one unknown.

And you apparently know how to solve it

$\$

 

[harpazo]

You are right: your post says you can't state the equation to be solved, not the other way around.

The problem statement you posted -- slightly edited

And the

is wrong.

You can't say

since they are not equal. And in addition it contradicts the next line -- which in itself is a very good start

because then from the problem statement it follows that Adam is 7x.

The remainder of the problem statement then tells you that in four years, when their ages are 5x+4 and 7x+4, those have a ratio 3/4. Voila the crucial equation of your friend (who was either mistaken or misquoted). One equation with one unknown.

And you apparently know how to solve it

$\$

Thanks