gail baked some muffins. She sold 2/7 of the muffins on Monday. She sold 1/3 more of the muffins on Tuesday than on Monday. What fraction of the muffins did Gail sell on the two days?
Monday: 2/7 = 6/21
Tuesday 2/7 * 4/3 = 8/21
so, on both days, ...
To solve this problem, let's break it down step by step.
Step 1: Determine the fraction of muffins Gail sold on Monday.
Gail sold 2/7 of the muffins on Monday.
Step 2: Determine the fraction of muffins Gail sold on Tuesday.
On Tuesday, Gail sold 1/3 more muffins than on Monday.
To find the fraction, we can add 1/3 to 2/7:
2/7 + 1/3.
To add these fractions, we need to find a common denominator. The smallest common denominator for 7 and 3 is 21.
Now, we can rewrite the fractions with the common denominator:
2/7 = (2/7) * (3/3) = 6/21.
1/3 = (1/3) * (7/7) = 7/21.
So, 2/7 + 1/3 = 6/21 + 7/21 = 13/21.
Therefore, Gail sold 13/21 of the muffins on Tuesday.
Step 3: Find the total fraction of muffins Gail sold on both days.
We can find the total fraction by adding the fractions from Monday and Tuesday together:
2/7 + 13/21.
To add these fractions, we need to find a common denominator. The smallest common denominator for 7 and 21 is 21.
Now, we can rewrite the fractions with the common denominator:
2/7 = (2/7) * (3/3) = 6/21.
13/21 remains the same.
So, 2/7 + 13/21 = 6/21 + 13/21 = 19/21.
Therefore, Gail sold a total of 19/21 of the muffins on both days.
To find the fraction of muffins Gail sold on the two days, we need to add the fractions she sold on Monday and Tuesday together.
First, let's calculate the fraction Gail sold on Monday. We know that she sold 2/7 of the muffins on that day.
Next, let's calculate the fraction she sold on Tuesday. We are given that she sold 1/3 more muffins on Tuesday than on Monday. To find out how much she sold on Tuesday, we need to add 1/3 of what she sold on Monday to what she sold on Monday.
To add fractions, we need to find a common denominator. In this case, the common denominator will be 7 × 3 = 21.
So, the fraction Gail sold on Tuesday is (2/7) + (1/3) × (2/7) = (2/7) + (2/21) = (6/21) + (2/21) = 8/21.
Finally, to get the fraction Gail sold on the two days, we add the fractions she sold on Monday and Tuesday: (2/7) + (8/21) = (6/21) + (8/21) = 14/21.
Therefore, Gail sold 14/21 of the muffins on the two days.