Red and Rock baked the same number of cakes. After Red sold 120 of his cakes and Rock sold 160 of his cakes, the ratio of Red’s remaining cakes to Rock’s remaining cakes was 5:3. How many cakes did both of them bake altogether?

cakes

Let Red’s remaining cakes be 5 units, and Rock’s remaining cakes be 3 units. So, the sum of both of their remaining cakes is (5 + 3 = 8) units, and the difference is (5 - 3 = 2) units.

Red and Rock baked the same number of cakes, so the difference between the number of cakes they sold is equal to the difference between the number of cakes they have left.

Then,

2 units = (160 – 120) = 40

1 unit = 40 ÷ 2 = 20

8 units = 8 × 20 = 160

The number of remaining cakes for both of them is 160.

Thus, the total number of cakes baked:

160 + 120 + 160 = 440