Georgia and Courtney share sweet in the ratio 4:7. Courtney gets 24 sweets than Georgia. How many sweets do they both get?

Georgia would get 32 sweets and Courtney would get 56 sweets.

Step-by-step explanation:

This question asks you to find equivalent fractions or ratio. They give us the starting ratio of 4:7, which represents that for every four sweets that Georgia receives, Courtney receives 7. They also tell us that Courtney gets 24 more sweets than Georgia. If we let 'x' equal the number of sweets that Georgia receives and 'x+24' equal the number of sweets that Courtney receives, then we can set up a proportion where 4/7 = x / (x+24). We then can use cross-multiplication and division to solve for the value of 'x'. In this case 4 (x + 24) = 7x. We use distribution to get 4x + 96 = 7x, then inverse operations (subtracting 4x from both sides) to get 96 = 3x, then inverse operations to divide 3 by both sides to get x=32. 32 would be the number of sweets Georgia receives and 32+24=56 would be the number of sweets that Courtney receives.