MODELING REAL
LIFE You and a
friend sign up for a
new volunteer project
to increase your
service hours. The
tables show your and
your friend's total
numbers of service
hours after different
numbers of weeks on
the new project. Who
initially has more
service hours? After
(how many weeks do
you and your friend
have the same total
number of service
hours?
Your Service Hours
Weeks, x
4
6
8
10
12
I
3
5
Total hours, y
15
20
25
30
9
35
14
16
Your Friend's Service Hours
Weeks, x
40
Total hours, y
10
14
18
22
(26)

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2022-08-25T16:32:33+02:00

The number of weeks you and your friend have the same total number of service hours is 2 2/3

The given parameters are:

Your friend

Initial = 8

Rate = 2

So, the function is

y = 8 + 2x

You

The points from the table are (4, 15) and (6, 20)

The equation of the function is

y = (y2 - y1)/(x2 - x1) * (x - x1) + y1

So, we have:

y = (20 - 15)/(6 - 2) * (x - 4) + 15

This gives

y = 1.25 * (x - 4) + 15

When the service hours are equal, we have:

1.25 * (x - 4) + 15 = 8 + 2x

Expand

1.25x - 5 + 15 = 8 + 2x

Collect the like terms

2x - 1.25x = -5 + 15 - 8

Evaluate the like terms

0.75x = 2

Divide by 0.75

x = 2 2/3

Hence, the number of weeks you and your friend have the same total number of service hours is 2 2/3

Read more about linear equations at:

https://brainly.com/question/14323743

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