Math Problems

[silveryhair]

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Find two positive numbers whose sum is 6 and whose product is 4?
Answer is: 3+/- sqr(5)


Part of $6,000 is invested at an annual rate of 8% and the rest at 6% annually. If x represents the amount invested at 6%, then the expression for the dollar amount of interest for both investments in one year is:
-0.02X + 480
Can anyone explain this? Thanks in advance! 🙂

 

[LaFleur]

Not gonna lie, I don't get the first one because sqrt(5) = 2.24 and 3*2.24 =/= 4 and 3+2.24 =/= 6...

Anyway, the second one I do get. So you have 6000$ and you're investing it to get some returns. If you invest all of your money at 8%, your return would be 6000*.08=480$. That is the maximum number of dollars you could get if you invested all of the money at 8%. However, you didn't invest all of the money at 8%. You also invested some x amount of money at 6%. The money invested at 6% is going to grow less than the money at 8% by a rate of .02*(money invested at 6%). That's where the -.02x comes from--because the money invested at 6% grows at a rate that is .02x less than the money invested at 8%. Therefore if 480$ is the maximum amount of money you can make if you invested all your money at 8%, and you didn't invest it all at 8% (you invested x amount at 6%), then the amount of money you would make in a year would be 480-.02x because x is growing at a rate that is .02 times smaller than the other sum of money at 8%, so you wouldn't be making 480$, you'd be making 480*.02x where x is the amount of th original 6000 that was invested at 6%.

I hope that's clear and thought out enough for you. Let me know if it doesn't make sense!

Sent from my ADR6300 using Tapatalk

 

[Streetwolf]

Two numbers:

x and y

Sum is 6:

x + y = 6

Product is 4:

xy = 4

Therefore x = 6 - y (from the first equation)

Plug into the second:

(6-y)y = 4
6y - y^2 = 4
y^2 - 6y + 4 = 0

y = 6 +- sqrt(36 - 16) / 2

y = 6 +- sqrt(20) / 2
y = 6 +- 2sqrt(5) / 2

y = 3 +- sqrt(5)

x has to be the other operation sign (if y is 3 PLUS then x is 3 MINUS).

 

[DQLEUCD]

Two numbers:

x and y

Sum is 6:

x + y = 6

Product is 4:

xy = 4

Therefore x = 6 - y (from the first equation)

Plug into the second:

(6-y)y = 4
6y - y^2 = 4
y^2 - 6y + 4 = 0

y = 6 +- sqrt(36 - 16) / 2

y = 6 +- sqrt(20) / 2
y = 6 +- 2sqrt(5) / 2

y = 3 +- sqrt(5)

x has to be the other operation sign (if y is 3 PLUS then x is 3 MINUS).

Yea, quadratic is a pain

(-b +/- (b^2 - 2ac)^1/2) / 2a

a = 1, b = 6 c = 4

 

[Streetwolf]

Yea, quadratic is a pain

(-b +/- (b^2 - 2ac)^1/2) / 2a

a = 1, b = 6 c = 4

- 4ac

 

[LaFleur]

Ahahahaha now I feel like an idiot. Totally read that wrong. Then again it was like 6 am my time...

Two numbers:

x and y

Sum is 6:

x + y = 6

Product is 4:

xy = 4

Therefore x = 6 - y (from the first equation)

Plug into the second:

(6-y)y = 4
6y - y^2 = 4
y^2 - 6y + 4 = 0

y = 6 +- sqrt(36 - 16) / 2

y = 6 +- sqrt(20) / 2
y = 6 +- 2sqrt(5) / 2

y = 3 +- sqrt(5)

x has to be the other operation sign (if y is 3 PLUS then x is 3 MINUS).

Sent from my ADR6300 using Tapatalk

 

[Pat Kelly]

Yea, quadratic is a pain

(-b +/- (b^2 - 2ac)^1/2) / 2a

a = 1, b = 6 c = 4

also b is -6. It doesn't matter in this case but you should always keep your signs straight otherwise you will get a different answer.

 

[THAPA]

Find two positive numbers whose sum is 6 and whose product is 4?
Answer is: 3+/- sqr(5)


Part of $6,000 is invested at an annual rate of 8% and the rest at 6% annually. If x represents the amount invested at 6%, then the expression for the dollar amount of interest for both investments in one year is:
-0.02X + 480
Can anyone explain this? Thanks in advance! 🙂

sometimes, in the first question it helps to use the answer choices and answer the question as in this example.
one can use the quadratic equation for this but if you are stuck with the equations or have less time , the best approach is to use the given answer choices and check them and see if it satisfies the question.