50 % of a number is 18 less than two-thirds of that number. Find the number.
Question
50 % of a number is 18 less than two-thirds of that number. Find the number.
Solution
Step 1: Let's denote the unknown number as x.
Step 2: According to the problem, 50% of the number (which is 0.5x) is 18 less than two-thirds of the number (which is 2/3x). We can write this as an equation:
0.5x = (2/3)x - 18
Step 3: To solve for x, we first need to get rid of the fractions. Multiply every term by 3 to do this:
1.5x = 2x - 54
Step 4: Now, let's isolate x by subtracting 1.5x from both sides of the equation:
2x - 1.5x = 54
0.5x = 54
Step 5: Finally, divide both sides by 0.5 to solve for x:
x = 54 / 0.5
x = 108
So, the number is 108.
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