SOLUTION: The sum of a negative number, 1/4 of the negative number, 7/16 of the negative number is -13 1/2. What is the negative number?

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Question 1071938: The sum of a negative number, 1/4 of the negative number, 7/16 of the negative number is -13 1/2. What is the negative number?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x be the negative number.

-(13 + 1/2) is equal to -27/2

you get:

x + 1/4 * x + 7/16 * x = -27/2

multiply both sides of this equation by 16 to get:

16x + 4x + 7x = (-27 * 16) / 2

combine like terms to get:

27x = (-27 * 16) / 2

divide both sides of this equation by 27 to get:

x = (-27 * 16) / (2 * 27)

the 27 in the numerator and denominator cancel out and you are left with:

x = -16/2

solve for x to get:

x = -8

that should be your number.

to confirm, replace x in your original equation with -8 to get:

x + 1/4 * x + 7/16 * x = -27/2 becomes:

-8 -8/4 - (7*8)/16) = -27/2.

simplify to get:

-8 - 2 - 7/2 = -27/2

multiply both sides of this equation by 2 to get:

-16 - 4 - 7 = -27

combine like terms to get:

-27 = -27

this confirms the solution is correct.

your solution is that the negative number you are looking for is equal to -8.