SOLUTION: the sum of a number and 1 is doubled and the result is added to 3 times the difference of the number and 2. the result is 61. what is the number?

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Question 1052302: the sum of a number and 1 is doubled and the result is added to 3 times the difference of the number and 2. the result is 61. what is the number?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the number.

2 * (x + 1) means the sum of a number and 1 is doubled.

3 * (x - 2) means 3 times the difference of the number and 2.

2 * (x + 1) + 3 * (x - 2) = 61 means the result of the first expression being added to the second expression is equal to 61.

you need to solve that equation.

start with 2 * (x + 1) + 3 * (x - 2) = 61

simplify to get 2 * x + 2 + 3 * x - 6 = 61

combine like terms to get 5 * x - 4 = 61

add 4 to both sides of the equation to get 5 * x = 65

divide both sides of the equation by 5 to get x = 13.

the number should be 13.

the sum of 13 and 1 is 14.
2 * 14 = 28

the difference of 13 and 2 is 11.
3 * 11 = 33

add 28 and 33 and you get 61.

if i translated the words correctly, then your answer is that the number is equal to 13.