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Call the numbers s for the smaller number and l for the larger. From the problem statement, s + l = 35 and l = 2s + 7. From the first of these equations, s = 35 - l. Substituting this expression into the second equation yields:

l = 2(35 - l) + 7. Multiplying out yields:

l = 70 - 2l + 7. Adding like terms after collecting the terms with "l" on the left yields:

3l = 77 or l = 77/3. Then from the first equation s = 35 - 77/3 = 28/3

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Q: What are the two numbers whose sum is thirty five and the larger number is seven more than twice the smaller number?
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The larger of two numbers is seventeen more than seven times the smaller number the larger number is also one hundred thirty-two more than two times the smaller number what are the numbers?

a = Larger numberb = Smaller numbera - 17 = 7b ... (1)a - 132 = 2b ... (2)Rearrange (2)a = 2b + 132 (3)Substitute (3) into (1)2b + 132 - 17 = 7b(Take 2b from both sides)132 - 17 = 5b5b = 115b = 23Substitute b = 23 into (2)a - 132 = 2 x 23a - 132 = 46a = 46 + 132a = 178


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