Four classmates are comparing the number of pages that they have read in a novel assigned for their language-arts class. Ken has read twice as many pages as Jenny. Alicia has read 18 pages more than Jenny and 11 pages more than Mark. Mark has read 38 pages. How many pages has each of the students read? Identify what you need to find out and plan how you will solve the problem. Show your work. Explain your answer.
Jenny = X Pages.
Ken = 2x
Alicia = x+18 = 38+11 = 49.
Mark = 38.
x+18 = 49
X = 49-18 = 31.
2x = 62.
To solve this problem, we need to find out how many pages each student has read. We are given the following information:
- Mark has read 38 pages.
- Ken has read twice as many pages as Jenny.
- Alicia has read 18 pages more than Jenny and 11 pages more than Mark.
Let's assign variables to represent the number of pages read by each student:
- Let M represent the number of pages Mark has read.
- Let J represent the number of pages Jenny has read.
- Let K represent the number of pages Ken has read.
- Let A represent the number of pages Alicia has read.
Now let's use the given information to create equations:
1. Mark has read 38 pages: M = 38.
2. Ken has read twice as many pages as Jenny: K = 2J.
3. Alicia has read 18 pages more than Jenny and 11 pages more than Mark: A = J + 18 = M + 11.
We can substitute the value of M from equation 1 into equation 3:
A = J + 18 = 38 + 11 = 49.
Now we have two equations:
1. K = 2J
2. A = 49
Since Ken has read twice as many pages as Jenny, we can substitute K in equation 1 with 2J:
2J = 2J
Now we can substitute the value of A from equation 2 into equation 3:
49 = J + 18.
Subtracting 18 from both sides:
31 = J.
Now that we have found the value of J, we can substitute it back into the other equations to find the values of K and A:
K = 2J = 2(31) = 62.
A = 49.
Therefore, Mark has read 38 pages, Jenny has read 31 pages, Ken has read 62 pages, and Alicia has read 49 pages.