Final answer:
The ratio in which sugar A and sugar B should be mixed to achieve a price of 56 per kg is 3:2. This is determined by setting up an equation based on the weighted average of the two prices and solving for the ratio.
Step-by-step explanation:
To find the ratio in which sugar A and sugar B should be mixed to get a mixture costing 56 per kg, we can use the concept of weighted average. The price of sugar A is 60 per kg, while sugar B is 50 per kg. We want a mixture that costs 56 per kg.
Let the amount of sugar A be x kg and the amount of sugar B be y kg. The total cost of sugar A is 60x, and the total cost of sugar B is 50y. The total cost of the mixture is 56(x+y). Setting up the equation based on the weighted average gives us:
60x + 50y = 56(x + y)
Expanding and simplifying the equation, we will have:
60x + 50y = 56x + 56y
4x = 6y
Dividing both sides by 2, to simplify the ratio:
2x = 3y
Therefore, x/y = 3/2.
The ratio in which sugar A and sugar B should be mixed to achieve a price of 56 per kg is 3:2.