# Math Help - Two problems

1. ## Two problems

1. An integer is seven more than another integer. Twice the larger integer is one less than the square of the smaller integer. Find the two integers.( There are 2 answers)

i used (x+7) and multiplied it w/ (x+7x2). Is that correct ?

2. A car dealership has been selling new cars at $6000 over the factory price. Sales have been averaging 80 cars per month. Because of inflation, the$6000 markup is going to be increased. The marketing manager has determined that, for every $100 increase, there will be one less car sold each month. What should the new markup be in order to maximize revenue ? How do you answer this ? 2. Originally Posted by myaa02 1. An integer is seven more than another integer. Twice the larger integer is one less than the square of the smaller integer. Find the two integers.( There are 2 answers) i used (x+7) and multiplied it w/ (x+7x2). Is that correct ? 2. A car dealership has been selling new cars at$6000 over the factory price. Sales have been averaging 80 cars per month. Because of inflation, the $6000 markup is going to be increased. The marketing manager has determined that, for every$100 increase, there will be one less car sold each month. What should the new markup be in order to maximize revenue ?

How do you answer this ?
For the first question, it's just a matter of translating the problem into math language and solving the equation. I'll do the first part for you:

$2(x+7) = x^2 - 1$

3. okay so i got $-x^2+2x+13$

do i use the quadratic formula ?

4. Originally Posted by myaa02
okay so i got $-x^2+2x+13$

do i use the quadratic formula ?
You should end up with

$x^2 - 2x + 15 = 0$,

which you can factor.

5. how do you factor again ? i forgot how to, sorry.

6. Originally Posted by myaa02
how do you factor again ? i forgot how to, sorry.
I made a mistake in my previous post, which I will correct here.

Your goal is to factor $x^2 - 2x - 15 = 0$ into

$(x - a)(x - b) = 0$. So you need to find two numbers whose product is -15 and whose sum is -2.

7. Originally Posted by icemanfan
I made a mistake in my previous post, which I will correct here.

Your goal is to factor $x^2 - 2x - 15 = 0$ into

$(x - a)(x - b) = 0$. So you need to find two numbers whose product is -15 and whose sum is -2.
+5 and -3

8. i got one integer , but i dont know how to get the other one ..

9. Originally Posted by myaa02
i got one integer , but i dont know how to get the other one ..
You factored $x^2 - 2x - 15 = 0$ to

$(x - 5)(x + 3) = 0$,

from which you get the two solutions 5 and -3. What are you confused about?

10. Originally Posted by icemanfan
You factored $x^2 - 2x - 15 = 0$ to

$(x - 5)(x + 3) = 0$,

from which you get the two solutions 5 and -3. What are you confused about?
arent both numbers supposed to work w/ the question when you sub them in ?

11. Originally Posted by myaa02
arent both numbers supposed to work w/ the question when you sub them in ?
Yes, and both of them do.

12. Originally Posted by icemanfan
Yes, and both of them do.
my bad I was just doing it wrong , thanks .. and can you help me w/ the other question ?

13. For the second question, your total profit is going to be

$(6000 + 100x)(80 - x)$.

Do you know how to maximize this function?

14. Originally Posted by icemanfan
For the second question, your total profit is going to be

$(6000 + 100x)(80 - x)$.

Do you know how to maximize this function?
by multiplying them together ?

15. Originally Posted by myaa02
by multiplying them together ?
That's a start. When you multiply it out, you will find that the function is a parabola. Where does the parabola achieve its maximum value?

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