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What is the cost of one carton of milk?

Mathematics

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Here are the solutions to the questions:

  1. What is the cost of one carton of milk?
  1. Define variables and set up equations based on the given information.

    Let $M$ be the cost of one carton of milk.  
    Let $Y$ be the cost of one carton of yoghurt.  
    From the problem:
    
    • One carton of yoghurt costs twice as much as one carton of milk: Y=2MY = 2M.
    • The total cost of 3 cartons of milk and 2 cartons of yoghurt is R24,50: 3M+2Y=R24.503M + 2Y = R24.50.
  2. Substitute the expression for YY from the first equation into the second equation.

    $$
    3M + 2(2M) = R24.50
    $$
    $$
    3M + 4M = R24.50
    $$
    $$
    7M = R24.50
    $$
    
  3. Solve for MM.

    $$
    M = \frac{R24.50}{7}
    $$
    $$
    M = R3.50
    $$
    The cost of one carton of milk is **R3,50**.
    

    2. What is the cost of one carton of milk and one carton of yoghurt?

  4. Use the cost of one carton of milk found in Question 1.

    Cost of one carton of milk ($M$) = $R3.50$.
    
  5. Calculate the cost of one carton of yoghurt (YY) using the relationship Y=2MY = 2M.

    $$
    Y = 2 \times R3.50
    $$
    $$
    Y = R7.00
    $$
    
  6. Calculate the total cost of one carton of milk and one carton of yoghurt.

    $$
    \text{Total cost} = M + Y
    $$
    $$
    \text{Total cost} = R3.50 + R7.00
    $$
    $$
    \text{Total cost} = R10.50
    $$
    The cost of one carton of milk and one carton of yoghurt is **R10,50**.
    
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