Question

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?​

Answer 1

Answer:  60 muffins

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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 = 2x+12 = 2*24+12 = 48+12 = 60
• Rebecca = 5x = 5*24 = 120

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

• 2x = 2*24 = 48
• 5x = 5*24 = 120
• 48:120 reduces to 2:5 after dividing both parts by 24

This helps confirm we have the correct answer.