Final answer:
To find out how many cupcakes Chloe must give to Claire so that the ratio of cupcakes becomes 1:2, we can set up a proportion based on the given ratios and solve for the unknown quantity. Chloe must give 13 cupcakes to Claire.
Step-by-step explanation:
To find out how many cupcakes Chloe must give to Claire, we can set up a proportion based on the given ratios. The original ratio is 4:5, which means Chloe has 4 cupcakes for every 5 cupcakes Claire has. Chloe initially had 24 cupcakes, so we can set up the following proportion:
4/5 = (24 - x)/x
Where x is the number of cupcakes Chloe gives to Claire. Cross multiplying, we get:
4x = 5(24 - x)
Expanding and rearranging the equation, we have:
4x = 120 - 5x
Combining like terms, we get:
9x = 120
Finally, dividing both sides by 9, we find that:
x = 13.33 (rounded to the nearest whole number)
Therefore, Chloe must give 13 cupcakes to Claire so that the ratio of Chloe's cupcakes to Claire's cupcakes becomes 1:2.