Suppose that on the shelf in a supermarket, the ratio of the number of small milk cartons ( 1 litre) to large milk cartons ( 2 litres) are in the ratio \( 5: 7 \). If there is a total of 180 cartons on the shelf, how many of each type are there?

Let's solve the problem step by step. **Given:** - The ratio of small milk cartons (1 litre) to large milk cartons (2 litres) is \( 5:7 \). - The total number of cartons is 180. **Let:** - \( s \) = number of small cartons - \( l \) = number of large cartons **From the ratio \( 5:7 \):** \[ \frac{s}{l} = \frac{5}{7} \] \[ s = \frac{5}{7}l \] **Total cartons:** \[ s + l = 180 \] **Substitute \( s \) from the ratio into the total:** \[ \frac{5}{7}l + l = 180 \] \[ \left(\frac{5}{7} + 1\right) l = 180 \] \[ \frac{12}{7}l = 180 \] \[ l = 180 \times \frac{7}{12} = 105 \] **Find \( s \):** \[ s = 180 - l = 180 - 105 = 75 \] **Answer:** - **Small cartons (1 litre):** 75 - **Large cartons (2 litres):** 105