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One-half the sum of two numbers is 12. One of the numbers is three more than two times the other number. What are the two numbers?

User Timebandit
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1 Answer

6 votes

Answer:

The two numbers are 17 and 7

Explanation:

Translate this word problem into a math equation

If we let x and y be the two unknown numbers

One-half the sum of two numbers is 12 ==>

  • sum of two numbers : x + y
  • one-half the sum of two numbers : (1/2)(x + y)
  • one-half the sum of two numbers is 12: (1/2)(x + y) =12


So one equation is 1/2(x + y) =12

Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12

x + y = 24 (1)

One of the numbers is three more than two times the other number:
x = 2y + 3

or

x - 2y = 3 (2)

Equation (2) - Equation (1) =>

x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21

3y = 21

y = 21/3

y = 7

With y = 7, substituting in equation 1 gives

x + y = 24

x + 7 = 24

x = 24-7

x = 17

The two numbers are 17 and 7





User Bjjer
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