Final answer:
To find a number such that one-fourth of the number is 50 less than two-thirds of the number, we can set up an equation and solve for 'x'. The value of 'x' is 120.
Step-by-step explanation:
To find a number such that one-fourth of the number is 50 less than two-thirds of the number, we can set up an equation. Let's call the number 'x'. According to the information given, we have the equation: 1/4x = (2/3x) - 50. To solve for 'x', we can first simplify the equation by multiplying both sides by 12 to remove the fractions: 3x = 8x - 600. Next, we can subtract 8x from both sides: -5x = -600. Finally, we can divide both sides by -5 to find the value of 'x': x = 120.