A trade bought corn for sh 20 per kilogram and beans for sh 60 per kilogram. She mixed the corn and beans and sold the mixture at sh 48 per kilogram. If she made a 60% Profit, determine the ratio corn: beans per kilogram in the mixture.
cost: 20c+60b
revenue: 48(c+b)
so, 48(c+b)=8/5 (20c+60b)
240c+240b = 160c+480b
80c = 240b
c/b = 240/80 = 3
that is, c:b = 3:1
How did you got 8/5?
To determine the ratio of corn to beans per kilogram in the mixture, we need to set up an equation based on the given information.
Let's assume that the trader buys x kilograms of corn and y kilograms of beans.
The cost of corn will be 20x shillings, and the cost of beans will be 60y shillings.
The total cost of the mixture will be the sum of the costs of corn and beans: 20x + 60y.
The trader sells the mixture at 48 shillings per kilogram, so the total revenue will be 48(x + y) shillings.
To calculate the profit, we need to subtract the total cost from the total revenue: Profit = Total Revenue - Total Cost.
Since the profit is 60% of the total cost, we can write the equation as:
Profit = 0.6 * (Total Cost)
48(x + y) - (20x + 60y) = 0.6 * (20x + 60y)
Expanding and simplifying the equation gives:
48x + 48y - 20x - 60y = 12x + 36y
Combining like terms:
28x - 12y = 12x + 36y
Rearranging terms:
16x = 48y
Dividing by 16:
x = 3y
This equation shows that for every kilogram of corn, there are 3 kilograms of beans in the mixture. Therefore, the ratio of corn to beans per kilogram in the mixture is 1:3.