This needs to be worked backwards.
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.
See previous post.
To find out how many pages each student has read, we need to determine the number of pages read by Ken, Jenny, Alicia, and Mark.
Let's assign variables:
Let J = the number of pages read by Jenny.
Since Ken has read twice as many pages as Jenny, Ken has read 2*J pages.
Alicia has read 18 pages more than Jenny, so Alicia has read J + 18 pages.
Alicia has also read 11 pages more than Mark, so Alicia has read Mark's pages plus 11: 38 + 11 = 49 pages.
To solve the problem, we'll work backward from the given information.
We are given that Mark has read 38 pages, therefore, Mark = 38.
Now we can substitute this value into the equation for Alicia's pages:
Alicia = Mark + 11
Alicia = 38 + 11
Alicia = 49
Next, we'll substitute the values for Alicia and Mark into the equation for Ken's pages:
Ken = 2*J
Ken = 2*(Jenny)
Finally, we know that Alicia has read J + 18 pages:
Alicia = Jenny + 18
Now we have a system of three equations:
Ken = 2*(Jenny)
Alicia = Jenny + 18
Alicia = 49
We can substitute the value of Alicia into the second equation:
49 = Jenny + 18
Jenny = 49 - 18
Jenny = 31
Using this value, we can substitute it back into the first equation to find Ken's pages:
Ken = 2*(31)
Ken = 62
So, Ken has read 62 pages, Jenny has read 31 pages, Alicia has read 49 pages, and Mark has read 38 pages.
To solve this problem, we need to find out how many pages each of the students has read.
Let's work backwards and go step by step to find the answer:
Step 1: We are given that Mark has read 38 pages.
Step 2: Alicia has read 11 pages more than Mark. So, Alicia has read 38 + 11 = 49 pages.
Step 3: Jenny has read fewer pages than Alicia. Given that Ken has read twice as many pages as Jenny, we can infer that Jenny has read half the number of pages as Ken. Let's denote the number of pages read by Jenny as 'J' and the number of pages read by Ken as 'K'. Therefore, K = 2J.
Step 4: Alicia has read 18 pages more than Jenny. Therefore, Alicia has read J + 18 pages.
Step 5: Since we know that Alicia has read 49 pages, we can set up the equation: J + 18 = 49
Step 6: Solve the equation to find the value of J:
J + 18 = 49
Subtract 18 from both sides: J = 49 - 18
J = 31
Step 7: Now that we know Jenny has read 31 pages, we can find the number of pages read by Ken:
K = 2J = 2(31) = 62
So, the four classmates have read the following number of pages:
- Jenny: 31 pages
- Ken: 62 pages
- Alicia: 49 pages
- Mark: 38 pages
Therefore, Jenny has read 31 pages, Ken has read 62 pages, Alicia has read 49 pages, and Mark has read 38 pages.