Question

For $7.52, you purchased 8 pens and highlighters from a local bookstore. Each highlighter costs $1.09 and each pen costs $.69. How many pens did you buy.

I've gotten down 1.09h + .69p = 7.52 but that's as far as I've gotten. If anyone could help me work this

Answer 1

i can.
it says you got 8 pens.
1.09h + .69(8) = 7.52
1.09h + 5.52 = 7.52

do you know what to do from here?

Answer 2

I thought that the 8 was for the combines amount of pens and highlighters?

Answer 3

This is for a study guide and the other questions in the lesson were about systems of equations, so because of the format of those, I'm completely lost when it comes to this problem.

Answer 4

no. it say 8 pens and highlighters.
i guess it seems confusing.. but i don't think they would do that.
to me it seems 8 pens, and some highlighters.
the other way it wouldn't make sense. do you see?


can you show me another one in the guide, though, so i can see?

Answer 5

I think that it a total of 8 pens and highlighters

Answer 6

because if it was 8 pens and some highlighters it would say that

Answer 7

Do you mean just the other problems in general or word problems, because that was the only word problem.

Answer 8

the word problem

Answer 9

These are the other problems, and I got kind of confused from the earlier examples in the book.

Answer 10

im doing number 9

Answer 11

yes, that's the one

Answer 12

then i'm not sure... sorry ^^

Answer 13

I think i got it. Silverr was right it is 8 pen and some highlighters

Answer 14

You have to multiply 8 x $1.09 (price)

Answer 15

So the first equation is 1.09h + .69(8) = 7.52?

Answer 16

yes

Answer 17

okay, than :)

1.09h + .69(8) = 7.52
1.09h + 5.52 = 7.52

Answer 18

ok whats next

Answer 19

then it would be 1.09h = 2?

Answer 20

1.09h + 5.52 = 7.52
7.52 - 5.52 = ?

Answer 21

so subtract 5.52 from 7.52 which is 2.00. so he has $2.00 left how many highlighters can he get?

Answer 22

Just 1?

Answer 23

yes

Answer 24

so the answer should be 1

Answer 25

I'm still confused on the end of the question though, because it asks how many pens you bought

Answer 26

Im verry sorry if i confused you but it is just 8 pens and highlighters. (:-/

Answer 27

i actually dont know how to solve it but your supposed to find the number of pens you can still afford with the highlighters

Answer 28

Oh, that's alright. Thank you so much for your help!

Answer 29

@phi

Answer 30

maybe phi can help ,

Answer 31

Ok, thanks again

Answer 32

It is poorly written, but they probably mean
h+p= 8
use that along with
1.09h + .69p = 7.52
to solve for h and p

Answer 33

I hope it's not too much to ask, but could you help walk me through that?

Answer 34

I feel like I have to move one of the variables to the other side with 7.52 to solve it?

Answer 35

you want to solve for p, so I would multiply the first equation
h+p= 8
by -1.09 (that means both sides , all terms)

then add the two equations. (this is using "elimination")

you said
I feel like I have to move one of the variables to the other side with 7.52 to solve it?

yes, you can take that approach (called "substitution")

But I would get used to elimination... it works better for hairier problems.

Answer 36

yeah, I tend to struggle a lot with the elimination method.

So it would be 1.09h + 1.09p = 8.72 for the second equation right?

Answer 37

you should get
-1.09h + -1.09p= -8.72
1.09h + . 69p = 7.52
---------------------
now add them

Answer 38

where did the negative terms come from on the top equation?

Answer 39

I multiplied by -1.09 so that when we add the "h" terms cancels

Answer 40

start with h+p=8
multiply by -1.09

Answer 41

So every time you do that you multiply with a negative term?

Answer 42

-.4p = -1.2

Answer 43

so p would equal 3?

Answer 44

I looked at the second equation
1.09h + . 69p = 7.52

and asked, "what do I add to 1.09h to make it go away? "
answer: -1.09h

then I looked at h+p=8
and asked, what do I multiply h by to get -1.09 h ?
answer: -1.09
so multiply the h+p=8 equation by -1.09
all terms, both sides to get
-1.09 h + -1.09p = -1.09*8

Answer 45

oh, ok that makes sense now

Answer 46

yes looks good. p= -1.2/-0.4 =3

Answer 47

does it matter which equation I substitute p into?

Answer 48

when I did it with h + p = 8, I got h =5

Answer 49

to find h ?
no. But one looks easier to use than the other i.e. h=5

but both equations will work.

Answer 50

though it's not obvious, the two equations can be thought of as equations of lines, and the solution is the point on both lines. So both equations will give the same answer for h, if you use p=3

Answer 51

I think I get it now. Thank you so much!

Answer 52

example
1.09h + . 69p = 7.52
1.09h + . 69*3 = 7.52
1.09h + 2.07 = 7.52
1.09h = 7.52-2.07
1.09h= 5.45
h= 5.45/1.07 = 5

Answer 53

obviously the same answer, but a lot more work than
3+h= 8
h= 5