document.write( "Question 51253: One-half of the sum of three consecutive multiples of 10 is 75. Find the three multiples of 10. \n" ); document.write( "

Algebra.Com's Answer #34383 by rchill(405) $\"\"$ $\"About$

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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. \n" ); document.write( "

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