one sixth of the sum of twice a number and 1 is the same as one quarter of the difference between three times the number and 1. find the number.
Just translate that confusing English into Math
"one sixth of the sum of twice a number and 1" ----> (2x + 1)/6
"is the same as " ----> =
"one quarter of the difference between three times the number and 1"
---- (3x - 1)/4
(3x - 1)/4 = (2x + 1)/6
times 12 to clear fractions
3(3x-1) = 2(2x + 1)
9x - 3 = 4x + 2
5x = 5
x = 1
The number is 1
Check: one sixth of the sum of twice a number and 1 = (1/6)(2 + 1) = 1/2
one quarter of the difference between three times the number and 1 = (1/4)(3-1) = 1/2
they are the same, my answer is correct
To find the number, let's break down the problem step by step:
Let's assume the number is represented by 'x.'
Translate the problem into an equation:
One-sixth of the sum of twice a number and 1 can be expressed as (1/6) * (2x + 1).
One-quarter of the difference between three times the number and 1 can be expressed as (1/4) * (3x - 1).
According to the problem, these two expressions are equal, so we can set them equal to each other:
(1/6) * (2x + 1) = (1/4) * (3x - 1)
Now we can solve this equation to find the value of x:
First, multiply both sides of the equation by 24 to eliminate the fractions:
24 * [(1/6) * (2x + 1)] = 24 * [(1/4) * (3x - 1)]
4 * (2x + 1) = 6 * (3x - 1)
Simplify the equation:
8x + 4 = 18x - 6
Rearrange the equation:
8x - 18x = -6 - 4
-10x = -10
Divide both sides by -10:
x = -10 / -10
Simplify:
x = 1
Therefore, the number is 1.