A candy store currently sells almonds for $8.50 per kilogram and peanuts for $4.50 per kilogram. It wants to create 20 kilograms of mixed nuts that will equivalently sell for $5.30 per kilogram. How many kilograms of almonds should they use?
To find out how many kilograms of almonds the candy store should use, we need to set up an equation based on the given information.
Let's assume the number of kilograms of almonds is represented by 'x'. Since the total weight of mixed nuts is given as 20 kilograms, the number of kilograms of peanuts will be 20 - x.
The cost of almonds per kilogram is $8.50, and the cost of peanuts per kilogram is $4.50. So, the total cost of almonds used will be 8.50x, and the total cost of peanuts used will be 4.50(20 - x).
The total cost of the mixed nuts will be the cost per kilogram multiplied by the total weight, which is $5.30 multiplied by 20. Therefore:
5.30 * 20 = 8.50x + 4.50(20 - x)
Simplifying the equation:
106 = 8.50x + 90 - 4.50x
Combining like terms:
106 - 90 = 8.50x - 4.50x
16 = 4x
Dividing both sides by 4:
16/4 = x
x = 4
Therefore, the candy store should use 4 kilograms of almonds to create 20 kilograms of mixed nuts.