Question

Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x) and would be split evenly between the two of them. Assume Bob works 3 hours. Create the function h(x), and indicate if Bob will make more money working alone or by teaming with Susie.

Answer 1

@mathstudent55

Answer 2

@jim_thompson5910

Answer 3

How much does Bob earn if he works for 3 hours and he's working alone?

Answer 4

I'm not sure...

Answer 5

well x = 3 and f(x) is Bob's income function

Answer 6

Would I plug that into x?

Answer 7

so f(3) represents how much money he earns alone

Answer 8

f(3) = ???

Answer 9

6x + 13?

Answer 10

yes, f(x) = 6x + 13

Answer 11

f(x) = 6x + 13

f(3) = 6(3) + 13 ... replace EVERY copy of x with 3 (since x = 3)

f(3) = ??

Answer 12

So 6(3)+13=31

Answer 13

he earns $31 on his own

Answer 14

now calculate h(3) to figure out how much both of them earn together (before they split it up)

Answer 15

How do I do that?

Answer 16

h(x) = f(x) + g(x)

h(3) = f(3) + g(3)

h(3) = ??

Answer 17

6?

Answer 18

so you'll need: f(3) and g(3)

you just found f(3). What is g(3) ?

Answer 19

Ohh

Answer 20

4(3)+18=30

Answer 21

so h(3) = ??

Answer 22

30(3)+31(3)?

Answer 23

remember we had h(3) = f(3) + g(3)

Answer 24

and we found f(3) = 31 and g(3) = 30

Answer 25

So 61?

Answer 26

since f(3) = 31, you replace all of "f(3)" with "31"

Answer 27

yes

Answer 28

that's their total combined income, but now we have to split it evenly amongst 2 people

Answer 29

How would I do that?

Answer 30

splitting is the same as dividing

Answer 31

Right, I got 15.5. But what do I do next, I mean?

Answer 32

example: you have 10 dollars to split amongst 2 people, so each gets 10/2 = 5 dollars

Answer 33

15.5 is too low

Answer 34

Oh sorry!

Answer 35

you take the combined income and divide it by 2

Answer 36

30.5

Answer 37

so which is better? Bob working on his own? or working with Susie?

Answer 38

On his own?

Answer 39

why on his own

Answer 40

Because he would receive more?

Answer 41

how much more

Answer 42

One dollar?

Answer 43

no

Answer 44

I'm so sorry , this is very new to me.

Answer 45

what is f(x) again?

Answer 46

3?

Answer 47

what does the function represent? Whose income?

Answer 48

Bob's

Answer 49

so f(3) represents what?

Answer 50

The amount of hours he worked?

Answer 51

x = 3 is the number of hours he worked (3 hours)

Answer 52

f(3) is the income he gets for working 3 hours

Answer 53

Right!

Answer 54

which was what?

Answer 55

31

Answer 56

so comparing 31 to 30.5, he loses $0.50 or 50 cents

It turns out that as x gets bigger, his loss gets bigger as well. So he's better off working alone.

Answer 57

Okay, got it. What would the equation be?

Answer 58

It's either h(x)=2x+5 or h(x)=10x+31

Answer 59

well remember that h(x) = f(x) + g(x)

Answer 60

you can replace f(x) with 6x+13 and replace g(x) with 4x+18

then simplify

Answer 61

(6x+13)+(4x+18)=10x+31

Answer 62

Jim thank you so much for your patience! I'm so grateful for you guys on OpenStudy!

Answer 63

you're welcome