P6 Math Heuristic #3 - Percentage (Answer)

Alexander and Marie had $4224 altogether. Alexander gave 30% of his money to Marie. Marie then spent 25% of her money on a synthesiser. In the end they had $3672 altogether. How much money did Alexander have at first?

1. Find the total amount spent:

• They started with $4224 and ended with $3672.

• The difference is the amount spent: $4224 - $3672 = $552

  
  

2. Relate the amount spent to Marie's spending:

• The problem states Marie spent 25% of her money on a synthesizer. This means the $552 spent represents 25% of the money Marie had after Alexander gave her some money.

  
  

3. Find the amount Marie had after Alexander gave her money:

• If $552 is 25% (or 1/4) of her money, then she had $552 x 4 = $2208 after Alexander's transfer.

  
  

4. Find the amount Marie had before Alexander gave her money:

• Let A be Alexander's initial money and M be Marie's initial money.

• We know A + M = $4224

• Alexander gave 30% of his money to Marie. So, Marie received 0.3A.

• Marie then had M + 0.3A = $2208

  
  

5. Set up equations to solve for A and M:

• Equation 1: A + M = 4224

• Equation 2: M + 0.3A = 2208

  
  

6. Solve the system of equations:

• From Equation 1, we can express M as: M = 4224 - A

• Substitute this into Equation 2: (4224 - A) + 0.3A = 2208

• Simplify: 4224 - 0.7A = 2208

• Subtract 4224 from both sides: -0.7A = 2208 - 4224

• -0.7A = -2016

• Divide by -0.7: A = -2016 / -0.7

• A = 2880

  
  

Therefore, Alexander had $2880 at first.