Question

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)















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

1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.

2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.

3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.

4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.

5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.

6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.

What is a system of equations?

A system of equations involves using more than one equation solved simultaneously.

Jesse's reading rate per day = 30 pages

Amir's reading rate per day = 35 pages

The number of pages read by Jesse, y = 30 + 30x

The number of pages read by Amir, y = 35x

Where x = the number of days they have been reading

Solving the equations:

y = 30 + 30x and y = 35x

35x  = 30 + 30x

35x - 30x = 30

5x = 30

x = 6 (30/5)

Jesse:

y = 30 + 30x

y = 30 + 30(6)

y = 210

Amir:

y = 35x

y = 35(6)

y = 210

Learn more about simultaneous equations at brainly.com/question/16763389

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