a manager bought some stamps. she gave 1/3 of them to a cashier and 1/5 of them to her secretary. if the secretary received 40 fewer stamps than the cashier, how many stamps did the cashier receive?
Let x = total number of stamps
1/3x - 1/5x = 40
Solve for x, the 1/3x.
20
To solve this problem, we can follow a step-by-step approach.
Step 1: Let's assume the total number of stamps that the manager bought is "x".
Step 2: The manager gave 1/3 of the stamps to the cashier, which is equivalent to (1/3) * x = x/3.
Step 3: The manager also gave 1/5 of the stamps to her secretary, which is equivalent to (1/5) * x = x/5.
Step 4: According to the problem, the secretary received 40 fewer stamps than the cashier. This can be represented as x/5 = (x/3) - 40.
Step 5: To solve this equation, we can multiply both sides by 15 to eliminate the fractions: 15 * (x/5) = 15 * ((x/3) - 40).
Simplifying this equation gives us: 3x = 5x - 600.
Step 6: Rearranging this equation gives us: 2x = 600.
Step 7: Dividing both sides by 2 gives us: x = 300.
Therefore, the manager bought a total of 300 stamps.
Step 8: To find out how many stamps the cashier received, we can substitute the value of x in the equation x/3. So, the cashier received (300/3) = 100 stamps.
Hence, the cashier received 100 stamps.