Chocos is a dish made from wheat suguar and cocoa Bertha is

Chocos is a dish made from wheat, suguar, and cocoa. Bertha is making a large pot of chocos for a party. Wheat (w) costs $5 per pound, sugar (s) costs $3 per pound, and cocoa (c) costs $4 per pound. She spends $48 on 12 pounds of food. She buys twice as much cocoa as sugar. How much wheat, sugar, and cocoa will she use (in pounds) in her dish?

Solution

Let the quantity of wheat sugar and cocoa be x, y and z lbs respectively.Then x+y+z = 12..(1), 5x + 3y + 4z = 48..(2) and z = 2y..(3) On substituting z = 2y in the 1st and the 2nd equation, we get x + y + 2y = 12 or, x + 3y = 12...(4) and 5x +3y .+ 4( 2y) = 48 or, 5x + 11y = 48...(5) .On multiplying both the sides of equation 4 by 5, we get 5x + 15 y = 60...(6). Now, on subtracting the 5th equation from the 6th equation, we get 5x + 15 y - 5x - 11y = 60 - 48 or, 4y = 12 so that y = 12/4 = 3. Then z = 2y = 6 and finally, on substituting these values of y and z in the 1st equation,we get x + 3 + 6 = 12 so that x = 12 - 9 = 3. We can verify the result by substituting x = 3, y = 3 and z = 6 in the 2nd equation. On substitution, we get 5*3 + 3*3 + 4*6 = 48 or, 15 + 9 + 24 = 48, which is correct. Thus, Bertha will use 3 lbs of wheat, 3 lbs of sugar and 6 lbs of cocoa in her dish.