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
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
\(\dfrac{x}{y}=\dfrac{6}{7}\\\\\Rightarrow x=\dfrac{6}{7}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
and
\(x+y=26\\\\\Rightarrow \dfrac{6}{7}y+y=26~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uing equation (i)}]\\\\\Rightarrow \dfrac{6y+7y}{7}=26\\\\\Rightarrow 13y=7\times26\\\\\Rightarrow y=\dfrac{7\times26}{13}\\\\\Rightarrow y=14.\)
From equation (i), we get
\(x=\dfrac{6}{7}\times14=6\times2=12.\)
Thus, the market sells 12 cans and 14 boxes of food.