Wren and Jenni are reading the same book. Wren is on page 14 and reads 2 pages every night.
Jenni is on page 6 and reads 3 pages every night.
After how many nights will they have read the same number of pages?
How many pages will that be?
To find out after how many nights they will have read the same number of pages, we need to find the least common multiple (LCM) of 2 and 3.
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, ...
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
As we can see, the first number they both have in common is 6, so after 6 nights they will have read the same number of pages.
To find out how many pages they will have both read, we can calculate: 6 pages + 2 pages/night * 6 nights = 6 + 12 = <<6+12=18>>18 pages.
Therefore, after 6 nights, Wren and Jenni will both have read 18 pages.
To find out after how many nights Wren and Jenni will have read the same number of pages, we can set up an equation:
Wren: Page 14 + 2n
Jenni: Page 6 + 3n
In this equation, "n" represents the number of nights.
Now, we set the two expressions equal to each other, since we want to find out when they will have read the same number of pages:
14 + 2n = 6 + 3n
To solve for "n," we'll subtract 2n from both sides:
14 = 6 + n
Next, subtract 6 from both sides:
8 = n
So, after 8 nights, Wren and Jenni will have read the same number of pages.
To find out how many pages they will have read at that point, we substitute n=8 into either equation:
Wren: Page 14 + 2n = 14 + 2(8) = 14 + 16 = 30
Therefore, after 8 nights, Wren and Jenni will have read a total of 30 pages.
To find out after how many nights Wren and Jenni will have read the same number of pages, we can set up an equation based on their reading rates.
Let's denote the number of nights as 'n'. Since Wren reads 2 pages every night, we can express the number of pages Wren has read after 'n' nights as: 2n + 14. Similarly, the number of pages Jenni has read after 'n' nights is: 3n + 6.
To find the number of nights when they have read the same number of pages, we set these two expressions equal to each other and solve for 'n':
2n + 14 = 3n + 6
Subtracting 2n from both sides:
14 = n + 6
Subtracting 6 from both sides:
8 = n
This means it will take 8 nights for Wren and Jenni to read the same number of pages.
To find out how many pages they will have read at that point, we substitute 'n' back into one of the equations. Using either of the initial expressions, we can find the number of pages when 'n' is 8:
2(8) + 14 = 16 + 14 = 30
Therefore, after 8 nights, Wren and Jenni will both have read 30 pages.