Question 101404: Find two consecutive integers such that the sum of 8 times the first integer and 7 times the second integer is 127
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! If you let x represent the first of the consecutive numbers, then the next consecutive
integer is 1 more than that. So the two consecutive integers can be represented by x and x+1.
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Then you are told that 8 times the first integer (that would be 8*x) and 7 times the second
integer (that would be 7*(x + 1) which multiplies out to 7x + 7) will add together to equal 127.
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So we can write the equation:
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8x + 7x + 7 = 127
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Adding the two terms that contain x results in:
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15x + 7 = 127
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Get rid of the 7 on the left side by subtracting 7 from both sides to get:
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15x = 120
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Solve for x by dividing both sides of this equation by 15, the multiplier of x to get:
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x = 120/15 = 8
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This tells you that the first integer is 8 so the next consecutive integer is 1 more than that
which means that it is 9. The answer is that the two integers are 8 and 9.
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Check this. 8 times 8 = 64 and 9 times 7 = 63. If you add 64 and 63 together you do get 127,
just as the problem said you should. So our answer checks OK.
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Hope this helps you to understand the problem.
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