anonymous
  • anonymous
one integer is 8 less than 4 times another integer. the product of the two integers is 60. What are the two integers? show work
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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slaaibak
  • slaaibak
Call the one integer x. call the other one y x = 4y - 8 xy = 60 Solve this.
anonymous
  • anonymous
can you help solve it?
slaaibak
  • slaaibak
Substitute the x=4y-8 into the second equation

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More answers

slaaibak
  • slaaibak
you will get (4y -8)y = 60 solve for y. then solve for x
anonymous
  • anonymous
Here's the process, my little sugarplum: Pick your favorite equation and your favorite variable in that equation. Solve for that variable. Now, use that to substitute into the OTHER equation. This will give you an equation with just one variable in it =) Solve for that variable, and you should just get a number. Now, you know one variable, so you can look back at either of the first equations and use that variable to solve for the other one.
anonymous
  • anonymous
i got y=-15 and x=-68?
anonymous
  • anonymous
im not positive that thats correct
anonymous
  • anonymous
no =( I don't think so.
slaaibak
  • slaaibak
Try again.
anonymous
  • anonymous
i dont know what i did wrong :/
anonymous
  • anonymous
Show me your work, okay?
anonymous
  • anonymous
ok 60=(4y-8)y 60=4y-8y 60/-4 = -4y/-4 y=-15
slaaibak
  • slaaibak
The problem lies in line 2
anonymous
  • anonymous
x= 4(-15)-8 x= -60-8 x=-68
anonymous
  • anonymous
what the problem? :o
anonymous
  • anonymous
(4y-8)y = 4y^2 -8y
anonymous
  • anonymous
distribute, sweet thang.
anonymous
  • anonymous
whoops! forgot the to square it. but then there are no like terms to combine how would we solve 60= 4y^2-8y
anonymous
  • anonymous
Well, that's a whole 'nother kind of problem, and I'm guessing you've actually had a lot of practice with it, but it can be tricky, I understand. The most common ways are factoring or quadratic formula. Sound familiar?
anonymous
  • anonymous
yes we have to move the 60 over so it becomes a zero so then we have the values a b c for quadratic equation
anonymous
  • anonymous
Good =) And actually, if you want to try factoring, it works nicely for this one. But I'm a fan of the quad formula, since it always works.
anonymous
  • anonymous
Yes =) Take out a common factor of 4 first though.
anonymous
  • anonymous
2 and 2
anonymous
  • anonymous
It makes it a lot easier.
anonymous
  • anonymous
Nooo show me your factoring, please.
anonymous
  • anonymous
4? isnt is 2 and 2 or 4 and 1?
anonymous
  • anonymous
noope. show me your factoring.
anonymous
  • anonymous
from 4y^2 -8y-60 = 0
anonymous
  • anonymous
4y*y ?
anonymous
  • anonymous
... okay you aren't good at factoring. That's okay. A lot of people aren't. Use the quadratic formula.
anonymous
  • anonymous
ok
anonymous
  • anonymous
I only say that because it's a whole different issue. We can work on it another time =)
anonymous
  • anonymous
ok after i do the quadratic equation i will get 2 different answers and those will be the answer to the problem right?
anonymous
  • anonymous
Re-read the problem and tell me if we have answered the question yet.
anonymous
  • anonymous
i did but i don't know won't that only find x and not y?
anonymous
  • anonymous
Right. Well actually, it finds y. Right?
anonymous
  • anonymous
i think so?
anonymous
  • anonymous
We wrote our two equations. We substituted into one of them and got an equation with just one variable, y. We're now using the quadratic formula to solve for that variable. It's a little bit confusing because we're getting two possibilities for that variable, but we're still only solving for the one variable. We don't know the second variable yet.
anonymous
  • anonymous
yes it seems so confusing i got fractions for both answers -1/12 and 1/20 is that correct?
anonymous
  • anonymous
=/ I don't know what mistake you made.
anonymous
  • anonymous
i dont know either :(
anonymous
  • anonymous
\[\frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-8) \pm \sqrt{(-8)^2-4(4)(-60)}}{2(4)}\]
anonymous
  • anonymous
You probably just messed up on a sign somewhere. Did you plug in like that?
anonymous
  • anonymous
oh i see what i did im sorry i was doing 2ac instead of 2a
anonymous
  • anonymous
Ah =)
anonymous
  • anonymous
x= 5 and x= -3?
anonymous
  • anonymous
Good. Except we were solving for y. It's important because of the next step.
anonymous
  • anonymous
When I go back and plug into the original equation, I want to make sure I plug into the right variable.
anonymous
  • anonymous
which variable do i plug into and do i use the 5 or -3?
anonymous
  • anonymous
Okay, when you do this kind of problem, it's not important which variable you solve for first. You picked y. That's fine. What's not fine is that halfway through the problem, you started calling it x. Do you understand? You were solving for y, and then you randomly renamed it x. This will cause problems. You solved for y. Don't rename it and there won't be any confusion. So now you know y, so obviously that's what you can substitute in for.
slaaibak
  • slaaibak
lol
anonymous
  • anonymous
sorry and yes we know 2 answer to y so then which one would you substitute for x?
anonymous
  • anonymous
Now, I understand that it's a little confusing that you get two answers for y. Try not to be confused by it. It just means that there are two possible answers to the question. One is when y=5 and the other is when y = -3. Whichever one you pick, you'll get an x value that goes along with that y value.
anonymous
  • anonymous
ok i chose 5 and plugged it into x=4y-8 and i got 12
anonymous
  • anonymous
Good =) So one possible solution is: x=12 y =5 Understand? Find the other possible solution.
anonymous
  • anonymous
the other possible solution is 55?
anonymous
  • anonymous
Woah there. Where'd 55 come from? You makin' guesses or somethin'?
anonymous
  • anonymous
whoops is it 63?
anonymous
  • anonymous
wait ! lol sorry im using the wrong equation
anonymous
  • anonymous
I have no idea what you're doing. Lol.
anonymous
  • anonymous
x= -20 ?
anonymous
  • anonymous
That's not wrong... but it's not a complete answer.
anonymous
  • anonymous
but isnt it x= 12, -20
anonymous
  • anonymous
The question asks you what the two variables are. The two variables are x and y. It turns out this problem has two possible answers, but a good answer should give me an x value and a y value.
anonymous
  • anonymous
but theres 2 x and y values
anonymous
  • anonymous
Ooooh, goodness. How to explain this...
anonymous
  • anonymous
lol i dont know what should i do? should i just leave 2 values for both variables?
anonymous
  • anonymous
Kind of.
anonymous
  • anonymous
Alright, stop worrying so much about the correct answer and let's just consider the question, okay?
anonymous
  • anonymous
ok
anonymous
  • anonymous
The question is talking about a couple of numbers. We called them x and y. And it told us something about those numbers.
anonymous
  • anonymous
It told us that that their product is 60. We wrote an equation about that. And it told us that one number was 8 less than 4 times the other. We wrote an equation about that.
slaaibak
  • slaaibak
Two solution sets. (5,12) and (-3, 20) That's all you need to know
anonymous
  • anonymous
And we're just trying to figure out two numbers that those things are true for.
anonymous
  • anonymous
Right?
anonymous
  • anonymous
right
anonymous
  • anonymous
So our answer should be two numbers. We happened to name them x and y, so our answer will look like x= y=
anonymous
  • anonymous
Well, it turns out, there's more than one possible pair of numbers.
anonymous
  • anonymous
yup so i just leave those 2 answers?
anonymous
  • anonymous
Right. And what are those two answers?
anonymous
  • anonymous
y= 5, -3 x= 12, -20
anonymous
  • anonymous
mmmm, I don't like how you wrote that.
anonymous
  • anonymous
why?
anonymous
  • anonymous
Is x=5 y = -20 a solution?
anonymous
  • anonymous
Try plugging it in if you need to check.
anonymous
  • anonymous
no i put y=5
anonymous
  • anonymous
and x= -20
anonymous
  • anonymous
Sorry, my mistake. Is y = 5 x=-20 a solution?
anonymous
  • anonymous
That's what I meant to ask.
anonymous
  • anonymous
wait no it isnt i just tried it out
anonymous
  • anonymous
Oh my. =(
anonymous
  • anonymous
Okay so... is y=5 still good?
anonymous
  • anonymous
It's not good when x=-20, we decided.
anonymous
  • anonymous
yes
anonymous
  • anonymous
Alright, why is it still good?
anonymous
  • anonymous
because when we plug it in -20=4(5)-8 it gives us 12 which is not equal to -20
anonymous
  • anonymous
Okay, that tells me why y=5 x=-20 is not a solution. Is y =5 bad in general then? Is x=-20 bad?
anonymous
  • anonymous
yes its bad the -20
anonymous
  • anonymous
wait no the 5 is bad
anonymous
  • anonymous
if we plug in -3 it will work
anonymous
  • anonymous
Ahhhhhh my point isn't that they are bad COMPLETELY. My point is just that they don't work TOGETHER.
anonymous
  • anonymous
oh sorry lol so i can just leave both numbers?
anonymous
  • anonymous
Your answer really needs to be two numbers that work together. What are two numbers that work together?
anonymous
  • anonymous
-3 and -20
anonymous
  • anonymous
Great. That's one answer.
anonymous
  • anonymous
As a SECOND. SEPARATE answer
anonymous
  • anonymous
you could do 5 and 12
anonymous
  • anonymous
So, to clarify, you wrote y = 5, -3 x = 12, -20 Which doesn't make it obvious which number goes with which. If you write it this way, it's much more clear y=5 x=12, and y=-3 x=-20
anonymous
  • anonymous
I know it probably seems unimportant, but writing it the first way really shows that you don't understand the question or your answer.
anonymous
  • anonymous
no it does seem important, thanks so much once again for your help it really means alot =D but i must go because its getting pretty late here
anonymous
  • anonymous
Well, if the problem was written as an actual real-life problem, it would be easier to explain why it was important. For example, maybe these numbers we're trying to solve for are x=pack of skittles purchased y = number of snickers bars purchased My answer would say something like "Oh, you EITHER bought 5 packs of skittles and 12 snickers bars OOOOR you bought -3 packs of skittles and -20 snickers bars" (shhh please ignore the fact that you can't buy a negative numer of snicker bars) Your answer would say something like, "You bought 5 packs of skittles and -3 packs of skittles. And the number of snickers bars you bought is 12. And also -20."
anonymous
  • anonymous
oh yeahhh! i like how you related it to real life lol and yeah so it really is possible to have negatives in our answer as long as it works together
anonymous
  • anonymous
Yeah, we can have negatives =) If we're solving real life problems, a lot of times we'll get negative answers. Those negative answers might make sense, or they might not and we might ignore them.
anonymous
  • anonymous
For example, if our problem was about money, then the positive answer might mean we made money and the negative answer might mean we lost money. However, if the problem we're solving is about how many children someone has and we got one negative answer and one positive answer, well we'd take the positive one and ignore the negative one because there is no way to have negative children.
anonymous
  • anonymous
yeah i see where you're going at and what you'tr trying to say. im sorry to end this convo but i have to leave to get some sleep because im up early in the morning tomorrow
anonymous
  • anonymous
Goodnight. =)
anonymous
  • anonymous
goodnight and thanks so much once again! you have been an amazing help!
anonymous
  • anonymous
My pleasure =)

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