Final answer:
By setting up a proportion using the ratio 3:4 and the given number of green grapes, which is 24, we can calculate that there are 32 black grapes in the fruit bowl.
Step-by-step explanation:
The student's question involves the concept of ratios in mathematics. Given the ratio of green grapes to black grapes as 3:4 and the fact that there are 24 green grapes, we can determine the number of black grapes. Since green and black grapes have a ratio of 3:4, for every 3 green grapes, there are 4 black grapes. We can use this ratio to set up a proportion to solve for the number of black grapes.
To find the number of black grapes, we can use the equivalent fractions:
3 green grapes / 4 black grapes = 24 green grapes / x black grapes
Cross-multiply to solve for x:
3x = 4 × 24
x = (4 × 24) / 3
x = 32
Therefore, there are 32 black grapes.