SOLUTION: What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126?

Question 215773: What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126?
Found 2 solutions by Earlsdon, drj:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the first (smallest) integer, then (x+2) is the next consecutive integer and (x+3) is the third (largest) consecutive integer.
"...the sum of twice the smallest integer and three times the largest is 126."

Subtract 6 from both sides.
Divide both sides by 5.
and ,
The three consecutive integers are: 24, 25, and 26.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126?

Step 1. Let n be an integer (smallest integer), n+1 and n+2 (largest integer) be the next two consecutive integers.

Step 2. Let 2n be twice the smallest integer.

Step 3. Let 3(n+2) be three times the largest integer.

Step 4. Then since the sum of twice the smallest and three times the largest is 126.

Step 5. The following steps will solve the equation in Step 4.

Subtract 6 from both sides of the equation

Divide 5 to both sides of the equation

With , then and

Check sum... which is a true statement.

Step 6. ANSWER: The numbers are 24, 25, and 26.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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