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1.)There are three consecutive odd integers.Three times the largest is seven times the smallest. What are the integers? 2.)Two numbers are consecutive even. If twice the smaller is 18 more than the larger,what are the numbers?

Sagot :

Shinalcantaraidn
1.) Three consecutive odd integers
Let 'x' be the first number
      'x+2' be the second number
     'x+4' be the third number
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-Three times the largest is seven times the smallest
7x = 3(x+4)
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Distribute 3 to the quantity (x+4)
7x = 3x + 12
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Transpose 3x to the left side of the equation
7x - 3x = 12
-----------------------------------
Combine like terms
4x = 12
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Divide the whole equation with 4
x = 3
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x = 3
x + 2 = 3 + 2
x + 2 = 5
x + 4 = 3 + 4
x + 4 = 7
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Therefore the three consecutive odd integers are 3, 5, 7.
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2.) Two numbers are consecutive even
Let 'x' be the first number
      'x+2' be the second number
-----------------------------------------------------
-If twice the smaller is 18 more than the larger
2x = (x+2) + 18
---------------------------------
Remove parenthesis
2x = x + 2 + 18
--------------------------------
Transpose x to the left side of the equation 
2x - x = 2 + 18
-------------------------------
Combine like terms
x = 20
-------------------------------
x = 20
x + 2 = 20 + 2
x + 2 = 22
------------------------------
Therefore the two consecutive even numbers are 20, 22.
Alvedeguzidn
1. The integers be x(smallest), x + 2 and x + 4(largest) since they are consecutive odd integers

3 times the largest is 7 times the smallest.

3(x + 4) = 7x

Multiply

3x + 12 = 7x

Transpose 6 and 7x

3x - 7x = -12

Subtract

-4x = -12

Divide by -4 both sides

-4x/-4 = -12/-4

Therefore

x = 3 (first odd integer)

Let's now substitute the value of x to determine the other two odd integers

second odd integer

3 + 2 = 5

third odd integer

3 + 4 = 7

Therefore the odd integers are 3, 5 and 7

2. Let the consecutive even be x and x + 2(largest)

Twice the smallest is 18 more than the larger

2x = (x + 2) + 18

Add 2 to 18

2x = x + 20

Transpose x

2x - x = 20

Therefore

x = 20

Let's now substitute the value of x to determine the value of the largest even

x + 2

20 + 2

Therefore

22 is the largest even and 20 is the smallest

I hope it helps