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Math Asked by a SnapAndSolve user · about 2 hours ago

The larger of two numbers is 4 more than the smaller number. If the sum of the numbers is 74, find the...

1. The larger of two numbers is 4 more than the smaller number. If the sum of the numbers is 74, find the numbers.
2. The larger of two numbers is seven less than three times the smaller number. If the sum of the numbers is 61, find the numbers.
3. The larger of two numbers is one more than four times the smaller number. If the sum of the numbers is 106, find the numbers.
4. One of two numbers is twice the smaller number. If 12 is subtracted from the larger number, the result is 7 more than the smaller number. Find the numbers.

Answer

  1. Let the smaller number be x. Then the larger number is x + 4. The equation is x + (x + 4) = 74. Solving gives 2x + 4 = 74, so 2x = 70, and x = 35. The numbers are 35 and 39.

  2. Let the smaller number be x. Then the larger number is 3x - 7. The equation is x + (3x - 7) = 61. Solving gives 4x - 7 = 61, so 4x = 68, and x = 17. The numbers are 17 and 44.

  3. Let the smaller number be x. Then the larger number is 4x + 1. The equation is x + (4x + 1) = 106. Solving gives 5x + 1 = 106, so 5x = 105, and x = 21. The numbers are 21 and 85.

  4. Let the smaller number be x. Then the larger number is 2x. The equation is 2x - 12 = x + 7. Solving gives x = 19. The numbers are 19 and 38.

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