<h3>
Answer: 60 muffins</h3>
=========================================================
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.
10 + (-5) = 10 - 5 = 5
-11 + 20 = 20 + (-11) = 20 - 11 = 9
102 + (-1) = 102 - 1 = 101
<span>-20 + 60 = 60 + (-20) = 60 - 20 = 40 </span>
