Question

An athlete is running in a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete is from the school is given by y (in miles), where x + 10y = 260 (Note: 0 ≤ x ≤ 10 and 0 ≤ y ≤ 26). Complete the steps below to understand how to find the intercepts of the equation and what they represent.

Answer 1

Hey there! Welcome to QuestionCove!!

Can you post the complete question?

Also something doesn't seem right if x is bound between 0 and 10, because if the total marathon is 26 miles, idek

But please post the rest of the question :)

Answer 2

An athlete is running in a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete is from the school is given by y (in miles), where x + 10y = 260 (Note: 0 ≤ x ≤ 10 and 0 ≤ y ≤ 26). Complete the steps below to understand how to find the intercepts of the equation and what they represent.

Use the relationship between x and y to find the time it takes for the runner to reach the school.

Use the relationship between x and y to find the distance between the runner and the high school at the start line.

If the runner ran for 40 minutes from the start line, what is the remaining distance between the runner and the school?

Answer 3

Perfect, so do you know how to find the x-intercept or y-intercept?

Answer 4

x is minutes and y is miles

Answer 5

Hint:

To find the x-intercept, set y=0 and solve for x

To find the y-intercept, set x=0 and solve for y

Answer 6

Yes, what you listed is the variables and what they represent in our equation

the x-intercept is when the line crosses the x-axis and this happens when y=0

And vice versa for the y-intercept, it's when it crosses the y-axis and that happens when x=0

Answer 7

So

x + 10y = 260

To find the x-intercept
Plug in y=0 and solve for x

To find the y-intercept
Plug in x=0 and solve for y

Answer 8

ok

Answer 9

260 represents?

Answer 10

so think about it, these intercepts are like the end points for our line

earlier you said that y was miles, so when we're 0 miles away from the school that means we've run the whole marathon, and you get x = 260
so that means... How long did it take you to run the marathon?

Answer 11

(they're the end points because we can't go into negatives or anything, like we can't keep running after we reach the school, or it's not possible to be running away from the school)
just to clarify

Answer 12

26 miles

Answer 13

Yes so basically

at x=0, we get y=260
So when we have run 0 minutes, we're at the beginning of the marathon, we're 26 miles away

And x=260, y=0
We have run for 260 minutes, and then we'll finally be 0 miles away from the school so it'll take 260 minutes to do the 26 miles

Answer 14

If the runner ran for 40 minutes from the start line, what is the remaining distance between the runner and the school?

Answer 15

So he ran for 40 minutes,
Just plug in x=40 into your equation and solve for y

Also this is why the 0 ≤ x ≤ 10 is a typo because it's not possible to limit ourselves to 10 minutes

Answer 16

but ye

x + 10y = 260

plug in x=40 and then the number you get for y is how many miles are left to run

Answer 17

22

Answer 18

Bingo!!

Answer 19

How much time will the runner take to complete half the distance between the start line and the high school?

Answer 20

So if the total distance is 26 miles, how much would half of that be?
Plug that in to y and solve for x

Answer 21

x+13=260

Answer 22

It's 10y, so you'll have to multiply by 10. Don't forget that

Answer 23

is the answer 20

Answer 24

not quite, how did you get to that?

x + 10y = 260

plug in y=13

Answer 25

x=
130 minutes.

Answer 26

Good job!

Answer 27

can you help me with another question?

Jason works as an administrative assistant for a local lawyer's office. The office is running low on pens and notepads, so he is asked to buy $150 worth of pens and notepads. Pens cost $1, and notepads cost $2. If the number of pens he buys is represented by x and the number of notepads he buys is represented by y, the situation can be given by x + 2y = 150, where 0 ≤ x ≤ 150, 0 ≤ y ≤ 75 and x and y can take only integer values.

Assuming that the stationery store is out of notepads, how many pens would Jason have to purchase to spend the entire amount he is given?

Assuming that the stationery store is out of pens, how many notepads would Jason have to purchase to spend the entire amount he is given?