SOLUTION: One-half of the sum of three consecutive multiples of 10 is 75. Find the three multiples of 10.

Algebra ->  Trigonometry-basics -> SOLUTION: One-half of the sum of three consecutive multiples of 10 is 75. Find the three multiples of 10.      Log On


   

Question 51253: One-half of the sum of three consecutive multiples of 10 is 75. Find the three multiples of 10.
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the first multiple of 10 (i.e., 10x). The next two consecutive multiples of 10 become 10(x+1) and 10(x+2). So our equation becomes %2810x%2B10%28x%2B1%29%2B10%28x%2B2%29%29%2F2=75. Now we just expand and simplify to solve. We first get %2810x%2B10x%2B10%2B10x%2B20%29%2F2=75. Combining like terms produces %2830x%2B30%29%2F2=75, which simplifies to 15x%2B15=75. Subtract 15 from both sides: 15x-15=75-15, which simplifies to 15x=60. Now divide both sidess by 15: 15x%2F15=60%2F15, which simplifies to x=4. That means the first number is 4*10, or 40; the next number is 10(4+1), or 50, and the next number is 60. Adding 40+50+60 produces 150; dividing 150 by 2 produces 75. That completes our check of our answer, which means our answer of 40, 50, and 60 is correct.