Math Problem Statement

had certain number of chocolates. Out of the 60% of the chocolates with A, he gave 80% of the chocolates to B and the remaining to C. If the difference between the number of chocolates left with A and the number of chocolates with B IS 144, then find the total number of chocolates A had.

Solution

Let's solve the problem step by step.

Step 1: Define the total number of chocolates A initially had

Let the total number of chocolates A initially had be xx.

Step 2: Calculate the chocolates left with A after giving away 60%

A gives away 60% of his chocolates, so he is left with: Chocolates left with A=0.4x\text{Chocolates left with A} = 0.4x

Step 3: Calculate the chocolates given to B

A gives 80% of the 60% of chocolates to B, so B receives: Chocolates given to B=0.8×0.6x=0.48x\text{Chocolates given to B} = 0.8 \times 0.6x = 0.48x

Step 4: Calculate the remaining chocolates from the 60% given to C

The remaining chocolates from the 60% were given to C, so C receives: Chocolates given to C=0.6x0.48x=0.12x\text{Chocolates given to C} = 0.6x - 0.48x = 0.12x

Step 5: Establish the given condition

The problem states that the difference between the number of chocolates left with A and the number of chocolates with B is 144: Difference=Chocolates with BChocolates left with A\text{Difference} = \text{Chocolates with B} - \text{Chocolates left with A} This gives us: 0.48x0.4x=1440.48x - 0.4x = 144

Step 6: Solve the equation

Simplify the equation: 0.08x=1440.08x = 144 Solve for xx: x=1440.08=1800x = \frac{144}{0.08} = 1800

Conclusion

The total number of chocolates A had is 1800\boxed{1800}.

Would you like more details on any step, or do you have any other questions?


Here are five related questions:

  1. If A had initially 2400 chocolates, how many would B receive?
  2. What would be the new difference if A gave 90% of his chocolates to B instead of 80%?
  3. How many chocolates did C receive in this problem?
  4. If the difference was 200 instead of 144, what would be the total number of chocolates A had?
  5. If A had 2000 chocolates, how many would be left with A after giving 60% away?

Tip: When solving word problems, carefully interpret each percentage step-by-step to avoid errors.