Question

To make a fruit punch orange juice and apple juice are mixed together in the ratio 3:1 Beth wanted to make 16 litres of punch and calculates that she would need 12 litres of orange juice.

Is this correct?
Justify your answer by calculation.

Answer 1

Beth is correct in her calculation; she would need 12 litres of orange juice to make 16 litres of fruit punch with a 3:1 ratio of orange juice to apple juice.

Step-by-step explanation:

To determine if Beth calculated correctly the amount of orange juice needed to make 16 litres of fruit punch with a ratio of 3:1 (orange juice to apple juice), we need to divide the total amount of punch by the sum of the ratio parts. The ratio parts add up to 3 (orange) + 1 (apple) = 4 parts total. For 16 litres of punch, each part would be 16 litres ÷ 4 = 4 litres.

Given the ratio of 3:1, we multiply the single part amount (4 litres) by the number of orange juice parts (3): 4 litres × 3 = 12 litres of orange juice. Similarly, for the apple juice, we multiply the single part amount (4 litres) by the number of apple juice parts (1): 4 litres × 1 = 4 litres of apple juice.

To determine if Beth's calculation is correct, we need to compare the ratio of orange juice to apple juice in the punch with the given quantities. If the ratio is 3:1, and Beth wants to make 16 liters of punch using 12 liters of orange juice, we can set up the proportion:

3/1 = 12/x

Cross-multiplying gives us 3x = 12, and solving for x we get x = 12/3 = 4.

Therefore, Beth would need 4 liters of apple juice to make 16 liters of punch with a ratio of 3:1.

Therefore, Beth is correct; she would need 12 litres of orange juice and 4 litres of apple juice to make 16 litres of fruit punch following the 3:1 ratio.