Solve
The reciprocal of two more than a number in three times the reciprocal of the number. Find the number
translate the English into Math ...
"two more than a number" ---- n+2
"The reciprocal of two more than a number" --- 1/(n+2)
"The reciprocal of two more than a number is " --- 1/(n+2) =
"The reciprocal of two more than a number is 3 times the reciprocal of the number"
---- 1/(n+2) = 3(1/n)
take it from there
To solve the problem, we need to translate the given sentence into an algebraic equation, and then solve for the unknown variable.
Let's assume the number is "x."
According to the problem, the reciprocal of two more than a number (x) is equal to three times the reciprocal of the number (x).
Step 1: Translate the problem into an equation:
The reciprocal of (two more than x) = 3 times the reciprocal of x
Step 2: Express the reciprocal of (two more than x):
1 / (x + 2)
Step 3: Express three times the reciprocal of x:
3 / x
Now, we have the equation:
1 / (x + 2) = 3 / x
Step 4: Eliminate the fractions by cross-multiplying:
x = 3(x + 2)
Step 5: Distribute on the right side of the equation:
x = 3x + 6
Step 6: Move all terms with x to one side:
x - 3x = 6
-2x = 6
Step 7: Solve for x by dividing both sides by -2:
x = 6 / -2
x = -3
Therefore, the number we're looking for is -3.