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?

Question

6 cans and 20 boxes
12 cans and 14 boxes
14 cans and 12 boxes
20 cans and 6 boxes

Answer 1

Let the number of cans sold be \( c \) and the number of boxes sold be \( b \). According to the problem, we have two key pieces of information:

1. The total number of cans and boxes sold is 26: \[ c + b = 26 \]

2. The ratio of cans to boxes is 6 to 7. We can express this as: \[ \frac{c}{b} = \frac{6}{7} \] This can be rearranged to: \[ 7c = 6b \]

Now, we can solve these two equations step by step. Let's start with the second equation by expressing \( b \) in terms of \( c \): \[ b = \frac{7}{6}c \]

Now substitute \( b \) in the first equation: \[ c + \frac{7}{6}c = 26 \]

To combine the terms, convert \( c \) into a fraction: \[ \frac{6}{6}c + \frac{7}{6}c = 26 \] \[ \frac{13}{6}c = 26 \]

Now, solve for \( c \): \[ 13c = 156 \] \[ c = 12 \]

Now that we have \( c \), substitute it back into the equation for \( b \): \[ b = 26 - c = 26 - 12 = 14 \]

So, the market sold 12 cans and 14 boxes.

Now let's verify the ratio to ensure correctness:

• Cans: 12
• Boxes: 14

The ratio is: \[ \frac{12}{14} = \frac{6}{7} \]

This confirms that the sales adhere to the given ratio.

Therefore, the market sold 12 cans and 14 boxes.