Helen and Rebecca baked some muffins in the ratio 2:5. After Helen baked another 12 muffins, the ratio become 1:2. How many muffins did Helen bake altogether?

Explanation:

x = some positive whole number

2x = amount Helen baked initially

5x = amount Rebecca baked initially

Notice that the ratio 2x:5x reduces to 2:5 after dividing both parts by x.

So (2x)/(5x) = 2/5

Helen then bakes another 12 muffins, bumping the 2x up to 2x+12. The ratio is now 1:2, which means,

(amount Helen bakes)/(amount Rebecca bakes) = 1/2

(2x+12)/(5x) = 1/2

2(2x+12) = 5x*1 cross multiply

4x+24 = 5x

24 = 5x-4x

24 = x

x = 24

From here, we then can say,

Helen baked 60 muffins and Rebecca baked 120 muffins. We see that 60:120 reduces to 1:2 after dividing both parts by the GCF 60.

Furthermore, note how

This helps confirm we have the correct answer.