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A market sells 6 cans of food for every 7 boxes of food. the market sold a total of 26 cans and boxes today. how many of each kind did the market sell? 6 cans and 20 boxes 12 cans and 14 boxes 14 cans and 12 boxes 20 cans and 6 boxes

Respuesta :

12 cans and 14 boxes is the answer

Answer:  The market sells 12 cans and 14 boxes of food.

Step-by-step explanation:  Given that a market sells 6 cans of food for every 7 boxes of food and a total of 26 and boxes are sold today.

We are to find the number of cans and boxes that the market sells.

Let x and y represents the number of cans and boxes respectively sold by the market.

Then, according to the given information, we have

[tex]\dfrac{x}{y}=\dfrac{6}{7}\\\\\Rightarrow x=\dfrac{6}{7}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]x+y=26\\\\\Rightarrow \dfrac{6}{7}y+y=26~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uing equation (i)}]\\\\\Rightarrow \dfrac{6y+7y}{7}=26\\\\\Rightarrow 13y=7\times26\\\\\Rightarrow y=\dfrac{7\times26}{13}\\\\\Rightarrow y=14.[/tex]

From equation (i), we get

[tex]x=\dfrac{6}{7}\times14=6\times2=12.[/tex]

Thus, the market sells 12 cans and 14 boxes of food.