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?
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:
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