If you place one full container of flour on one pan of a balance scale and a similar container 3/4 full and a 1/3-pound weight on the other pan, the pans balance. How much does the full container of flour weigh?
1/4 container = 1/3 pound
4/4 container = 1 container = 4/3 pound
=
1 1/3 pound
To solve this problem, let's break it down step by step.
Step 1: Set up the equation.
Let's assume the weight of the full container of flour is 'x' pounds. The weight of the 3/4 full container of flour will then be 3/4 * x pounds.
According to the given conditions, the weight of the 3/4 full container of flour and the 1/3-pound weight should balance the weight of the full container of flour. We can express this equation as:
3/4 * x + 1/3 = x
Step 2: Solve the equation.
To solve the equation, we need to get rid of the fractions by finding a common denominator. In this case, the least common multiple (LCM) of 4 and 3 is 12.
Multiplying through by 12, we get:
9x + 4 = 12x
Simplifying the equation, we have:
4 = 12x - 9x
4 = 3x
Dividing both sides by 3, we find:
x = 4/3 or 1 1/3 pounds
Therefore, the full container of flour weighs 1 1/3 pounds.