Question 267454
two boys' ages total 24. four less than six times the younger boy's age equals five more than three times the older boy's age. what are their ages?
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Here is the way to interpret analytically what that problem says:

1. Add the younger boys age and the older 
   boy's ages together and you get 24. 
2. Take the younger boy's age.
3. Multiply it by 6
4. Make what you got 4 less by subtracting 4 from it.
5. Take the older boy's age.
6. Multiply it by 3.
7. Make what you got 5 more by adding 5 to it
8. What you got in step 4 is equal to what you got in step 7.

First do it with variable x for the younger boy's age and
y for the older boy's age:

1. Add the younger boys age and the older                      
   boy's ages together and you get 24.                        That's x+y=24
2. Take the younger boy's age.                                That's x.
3. Multiply it by 6.                                          That's 6x.
4. Make what you got 4 less by subtracting 4 from it.         That's 6x-4
5. Take the older boy's age.                                  That's y.
6. Multiply it by 3.                                          That's 3y. 
7. Make what you got 5 more by adding 5 to it.                That's 3y+5 
8. What you got in step 4 is equal to what you got in step 7. That's 6x-4=3y+5

Take the system of two equations in two variables from
steps 1 and 8:

{{{system(x+y=24,6x-4=3y+5)}}}

Simplify it and solve it by substitution or elimination.

Answer: x=9, y= 15.  The youger boy is 9 and the older boy is 15.

Now check it with the numbers with the same 8 sentences:

1. Add the younger boys age and the older                      
   boy's ages together and you get 24.                        That's 9+15=24
2. Take the younger boy's age.                                That's 9.
3. Multiply it by 6.                                          That's 54.
4. Make what you got 4 less by subtracting 4 from it.         That's 50
5. Take the older boy's age.                                  That's 15.
6. Multiply it by 3.                                          That's 45. 
7. Make what you got 5 more by adding 5 to it.                That's 50 
8. What you got in step 4 is equal to what you got in step 7. That's 50=50 



Steps 1 and 8 show that the answer is correct.

Try to break word problems into steps like the above.

Edwin</pre>