Decrease a number by 5, divide the result by 2, then add 17 and multiply by 5. If the final result is 100, with what number did you start?
[( x-5)/2 + 17] * 5 = 100
Divide both sides by 5.
(x - 5)/2 + 17 = 20
Subtract 17 from both sides.
(x - 5)/2 = 3
Multiply both sides by 2.
x - 5 = 6
Add 5 to both sides.
x = 11
To find the number you started with, we need to reverse the operations.
Let's start by solving the equation to find the unknown number:
Step 1: Reverse the multiplication operation by dividing the final result (100) by 5.
Final result divided by 5 = 100 ÷ 5 = 20
Step 2: Reverse the addition operation by subtracting 17 from the previous result.
Result minus 17 = 20 - 17 = 3
Step 3: Reverse the division operation by multiplying the previous result by 2.
Result multiplied by 2 = 3 x 2 = 6
Step 4: Reverse the subtraction operation by adding 5 to the previous result.
Result plus 5 = 6 + 5 = 11
Therefore, the number you started with is 11.