Question

I really need help, please. I have question one but I can't figure out the rest.

4.3.4 Practice: Solving Systems of Linear Equations by Substitution
Practice
M/J Grade 8 Pre-Algebra Sem 1
Points Possible:10
Name:
Caine Jones
Date:


Your Assignment
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)



2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)








3. Write the system of equations using your answers from questions 1 and 2.
(2 points)




4. You will use substitution to solve this system. Which variable will you substitute for and why? Show the equation that results from the substitution. (2 points)




5. Solve the system of equations. Show your work. (2 points)




6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)

Answer 1

Answer: i got number 1 :)

6 days

210 pages

Explanation:

As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.

Now since he reads 35 pages per day.

Then mathematically;

y = 35x

For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)

To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that

Also; y = 30(x + 1)

Equating the two situations

35x = 30(x + 1)

35x = 30x + 30

35x -30x = 30

5x = 30

x = 30/5

x = 6 days

This means that it will take Amir 6 days to catch Jese.

The number of books they would have read by then is y = 35x = 30(x + 1)

= 35 * 6 or 30(6+1)

= 210

Answer 2

1. The equation to represent the number of pages Amir has read is y = 35x, where x is the number of days Amir has been reading and y is the number of pages he has read.

2. Let's say that Jesse started reading on Saturday, and Amir started reading on Sunday. If x is the number of days Amir has been reading, then Jesse has been reading for x + 1 days. The equation to represent the number of pages Jesse has read is y = 30(x + 1), where y is the number of pages Jesse has read.

3. The system of equations is:

y = 35x

y = 30(x + 1)

4. We will substitute y in the second equation with y from the first equation. We can do this because both equations represent the number of pages each person has read. So we have:

35x = 30(x + 1)

5. Solving for x:

35x = 30x + 30

5x = 30

x = 6

So it will take Amir 6 days to catch up to Jesse.

To find the number of pages they have read, we can use either of the original equations. If Amir has been reading for 6 days, he has read:

y = 35x = 35(6) = 210 pages

If Jesse has been reading for 7 days (one day more than Amir), he has read:

y = 30(x + 1) = 30(7) = 210 pages

So when Amir catches up to Jesse, they will both have read 210 pages.

6. Amir will catch up to Jesse in 6 days. At that time, they will each have read 210 pages.