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Chocos is a dish made from wheat, sugar, and cocoa. Bertha is making a large pot of chocos for a party. Wheat(w) cost $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.

Respuesta :

The question is incomplete, complete question 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?

Answer:

She uses 3 pounds of wheat, 3 pounds of sugar and 6 pounds of cocoa in her dish.

Step-by-step explanation:

Given,

Total amount of spent money = $ 48

Total quantity of ingredients = 12 pounds

Let the quantity of wheat, sugar and cocoa she buys be x, y z pounds respectively.

[tex]\therefore x+y+z=12\ equation 1\\and\ 5x+3y+4z=48\ equation2[/tex]

And according to question, quantity of cocoa is 2 times of sugar.

[tex]\therefore z=2y[/tex]

Now substituting the value of z in equation 1and 2, we get;

[tex]x+y+2y=12\\x+3y=12\ equation3[/tex]

[tex]5x+3y+4\times2y=48\\5x+3y+8y=48\\5x+11y=48\ equation\ 4[/tex]

Now multiply equation 3 by 5 and then subtract equation 4 from it.

[tex]5(x+3y)=5\times12\\(5x+15y=60)-(5x+11y=48)\\4y=12\\y=\frac{12}{4}=3[/tex]

[tex]\therefore z=2y=2\times3=6[/tex]

And substituting the value of y in equation 3, we get;

[tex]x+3y=12\\x+3\times3=12\\x+9=12\\x=12-9=3[/tex]

Thus the amount she uses is 3 pounds of wheat, 3 pounds of sugar and 6 pounds of cocoa in her dish.

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