# 4 number have a total of 92.The first # is twice the 2nd # and the 3rd # is 4 more than the sum of the first two. The 4th# is 3 less than the difference of the first 2 numbers.What are the numbers?

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by miana

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by miana

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Let x be the second number.

Representation:

First number = 2x (twice the second number)

Second number = x

Third number = (2x+x) + 4 (four more than the sum of the first two numbers)

Fourth number = (2x-x) - 3 (three less than the difference of first two numbers)

Total of the four numbers = 92

Equation:

2x + x + (2x+x+4) + (2x-x-3) = 92

2x + x + 3x + 4 + x-3 = 92

Combine the like terms:

2x + x + 3x + x + 4 - 3 = 92

7x +1 = 92

7x = 92-1

__7x __= __91__

7 7

x = 13

The numbers are:

first number = 2x

= 2(13)

= 26

second number = x

= 13

third number = 2x + x + 4

= 2 (13) + 13 + 4

= 26 + 13 + 4

= 43

fourth number = 2x-x-3

= 2(13) - 13 - 3

= 26 - 13- 3

= 10

To check:

26 + 13 + 43 + 10 = 92

92 = 92

Representation:

First number = 2x (twice the second number)

Second number = x

Third number = (2x+x) + 4 (four more than the sum of the first two numbers)

Fourth number = (2x-x) - 3 (three less than the difference of first two numbers)

Total of the four numbers = 92

Equation:

2x + x + (2x+x+4) + (2x-x-3) = 92

2x + x + 3x + 4 + x-3 = 92

Combine the like terms:

2x + x + 3x + x + 4 - 3 = 92

7x +1 = 92

7x = 92-1

7 7

x = 13

The numbers are:

first number = 2x

= 2(13)

= 26

second number = x

= 13

third number = 2x + x + 4

= 2 (13) + 13 + 4

= 26 + 13 + 4

= 43

fourth number = 2x-x-3

= 2(13) - 13 - 3

= 26 - 13- 3

= 10

To check:

26 + 13 + 43 + 10 = 92

92 = 92