You bought two varieties of rice, costing 5 cents per ounce
and 6 cents per ounce each, and mixed them in some ratio. You then
sold the mixture at 7 cents per ounce, making a profit of 20 percent.
What was the ratio of the mixture?
let's say that for each ounce of 5-cent rice, you buy k ounces of 6-cent rice.
7(1+k) = (5+6k)(6/5)
k = 5
To find the ratio of the mixture, let's work through the problem step by step:
1. Let's assume the ratio of the two varieties of rice is x : y, where x and y are positive integers representing the amount (in ounces) of each rice variety.
2. If the first variety costs 5 cents per ounce, the total cost of the first variety would be 5x cents.
3. Similarly, the second variety costs 6 cents per ounce, so the total cost of the second variety would be 6y cents.
4. The total cost of the mixture would be the sum of the costs of the two varieties: 5x + 6y cents.
5. According to the problem, the mixture is sold at 7 cents per ounce, meaning the total revenue from selling the mixture would be 7(x + y) cents.
6. The profit earned is calculated by subtracting the total cost from the total revenue: 7(x + y) - (5x + 6y) cents.
7. We are given that the profit is 20% of the cost, which can be written mathematically as: (7(x + y) - (5x + 6y)) = 0.20(5x + 6y).
8. Simplifying the equation, we get: 7x + 7y - 5x - 6y = 0.20(5x + 6y).
9. Further simplifying, we have: 2x + y = 0.20(5x + 6y).
10. Expanding the equation gives: 2x + y = 1x + 1.2y.
11. Rearranging the terms, we get: 2x - 1x = 1.2y - y.
12. Simplifying, we have: x = 0.2y.
13. We know that x and y are positive integers, so let's choose a value for y and calculate the corresponding value for x.
14. Let's try y = 5. Substituting this into the equation from step 12, we get: x = 0.2 * 5 = 1.
15. The ratio of the mixture is therefore 1 : 5.
So, the ratio of the two varieties of rice in the mixture is 1 : 5.