SOLUTION: The larger of two numbers is eight more than three times the smaller number. The sum of the two numbers is fifty-two. Find the two numbers.

Algebra.Com
Question 1182249: The larger of two numbers is eight more than three times the smaller number. The sum of the two numbers is fifty-two. Find the two numbers.
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x and 52-x are the numbers
x=3(52-x)+8
x=156-3x+8
4x=164
x=41
52-x=11
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


In the solution from the other tutor, the problem is set up using the second given statement (the sum of the two numbers is 52) and the problem is then solved using an equation based on the first given statement.

That solution method is fine -- but not the most obvious method. Most students would choose to set up the problem using the first statement and then use the second statement to make an equation to solve to find the answer.

The larger of two numbers is eight more than three times the smaller number:

let the smaller number be x
then the larger number is 3x+8

The sum of the two numbers is fifty-two:

x+3x+8=52
4x+8=52
4x=44
x=11

ANSWER:

The two numbers are
x=11
3x+8=33+8=41

Both methods are equally good. When you have similar problems to solve, try both methods and see what works best for you.
RELATED QUESTIONS

The larger of two numbers is eight more than the smaller number. Their sum is twenty-two. (answered by lynnlo)
The sum of two numbers is ten. Three times the larger number is three less than eight... (answered by josgarithmetic)
the sum of two numbers is ten. three times the larger number is three less than eight... (answered by CubeyThePenguin)
The sum of two numbers is 50. the larger number is five more than eight times the smaller (answered by macston)
The larger of two numbers is 23. If three times the larger is 5 more than eight times the (answered by Maths68)
Number Problem: The sum of two numbers is 70. The larger number is two more than three... (answered by rfer)
The larger of two numbers is three more than five times the smaller. If the sum of the... (answered by RAY100)
the sum of two numbers is two. the difference between eight and twice the smaller number (answered by checkley71,ankor@dixie-net.com)
The sum of two integers is twenty-two. Eight times the smaller integer is fifty-six more... (answered by josmiceli)