Just a few more, instructions/pointers needed!

[opensesame]

I hope no one gets ticked about my post. I am really pressed for time and need to learn a lot again really fast. Heres my position. I am trying to get my dream job, which does not involve algebra. But the assessment test does include algebra questions. I have taken three years of algebra, but haven't "done" it for the last seven years.

Now I have to try to re-learn a lot before Wednesday. Everyone is probably thinking, "Good luck!". Well, you would be surprised at what I can do when motivated!

I have a few quick questions to start. One of my practice questions asked what the perimeter of something was. I have found out how to find the perimeter already. Now I need to find out how to find the product of something. Specifically:

What is the "product of two digits"? What is meant by that?

I apologize for slamming you guys with something like this. I am almost certain that its frowned upon. Here is the specific practice question, if it will help, please if you are going to help. Try to provide something in the easiest terms you can so that I can try to gain a full understanding. I appreciate all and any help you can give. Even if its a link to some kind of tutorial.

The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are _______?

The answer to the question above is "(45, 54)". Since I don't know how to find the product, I cannot find out how to come up with the answer.

Thank you!

 

[Guest]

The product is what you get when you multiply your numbers. I take it that's what you're needing?
Or, to put it another way, product is to multiplication as sum is to addition.

I hope you do alright. I know how hard it is to relearn stuff you've forgotten!

 

[opensesame]

thank you that was perfect !!!!

I appreciate it very much
.

 

[Guest]

You're welcome!

 

[stapel]

Re: What do they mean by "the product of two digits&quo

The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are _______?

In full, they probably had the following in mind:

. . . . .Let the first two-digit number be 10a + b,
. . . . .and the second two-digit number be 10c + d.

You need to work with the digits, so you need to have variables for each. Also, in any two-digit number, the "first" digit is the tens, so the value of that "place" is 10 times whatever the digit is. For instance, twenty-seven is "27", which means 10(2) + 7.

. . . . .Since the sums are 9, then a + b = 9 and c + d = 9.
. . . . .This means that we can solve for one of the
. . . . .digits in terms of the other; namely, b = 9 - a
. . . . .and d = 9 - c.

. . . . .Since it doesn't matter which number we use
. . . . .(the problem specifies "either"), then let's work
. . . . .with the first number, 10a + b.

. . . . .Translating the long word sentence, we get:

. . . . .square of first digit: a²
. . . . .product of both digits: ab
. . . . ."minus": a² - ab
. . . . .square of second digit: b²
. . . . ."plus": a² - ab + b²
. . . . ."is 21": a² - ab + b² = 21

. . . . .Since b = 9 - a, then:

. . . . .a² - a(9 - a) + (9 - a)² = 21

. . . . .a² - 9a + a² + 81 - 18a + a² = 21

. . . . .3a² - 27a + 81 = 21

. . . . .a² - 9a + 27 = 7

. . . . .a² - 9a + 20 = 0

. . . . .(a - 4)(a - 5) = 0

. . . . .a = 4 or a = 5

. . . . .If a = 4, then b = 9 - a = 5.
. . . . .If a = 5, then b = 9 - a = 4.

. . . . .Either way, we get the digits "5" and "4", so the
. . . . .two numbers must be "54" and "45".

As you can see, there is much more involved then just the meaning of the word "product". You'll need to learn about variables, how to "translate" word problems, and how to set up and solve equations (including quadratics).

My best wishes to you on your job!

Eliz.

 

[opensesame]

Hello Guys I have answered all of my questions except 3 of them. Thank you for all of your help so far. It has gotten me to this point

I am tired at the moment so this maybe part of my issue. again these are just examples

I was hoping a few of you might be able to show me how you would come up the answer. My test is tomorrow and its 10:12 pm right now. If I don't crash, I wont be rested for the last minute studying tomorrow.

anywho, please if you can. provide the easiest instructions you can think of. I need to learn quickly lol.

#1)If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________? THE ANSWER WAS= (7,17)

I am wondering if the rate can be calculated using a simple method, which i tried googling and only found hard methods lol. at least to me. I dont even know what the 7,17 is standing for at this point, in other words MPH ?

I think I figured out the above question anyway, but I am hoping for an easier way to work the math.


#2)The sum of two numbers is 17 and the sum of their square is 145. Find the larger number. THE ANSWER WAS= (9)

I think the above question should be easier than I am making it out to be. again Im tired.

#3)A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is $91. How much is invested at 8%. THE ANSWER WAS= ($700)

I have not really worked with interests before, so maybe I am thinking too hard since it says the word interest.

I bet these are pretty easy to you guys :lol:

The good news is that this will be my last question for this test preparation. I appreciate your guys help thus far, and in advance.

Its just hard trying to hold a full time job, then studying all night long for preparation of a new one. I am about beat

YOU GUYS ARE SAVING ME HOURS OF RESEARCH. thank you, thank you, thank you

 

[Mrspi]

Hello Guys I have answered all of my questions except 3 of them. Thank you for all of your help so far. It has gotten me to this point

I am tired at the moment so this maybe part of my issue. again these are just examples

I was hoping a few of you might be able to show me how you would come up the answer. My test is tomorrow and its 10:12 pm right now. If I don't crash, I wont be rested for the last minute studying tomorrow.

anywho, please if you can. provide the easiest instructions you can think of. I need to learn quickly lol.

#1)If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________? THE ANSWER WAS= (7,17)

I am wondering if the rate can be calculated using a simple method, which i tried googling and only found hard methods lol. at least to me. I dont even know what the 7,17 is standing for at this point, in other words MPH ?

I think I figured out the above question anyway, but I am hoping for an easier way to work the math.


#2)The sum of two numbers is 17 and the sum of their square is 145. Find the larger number. THE ANSWER WAS= (9)

I think the above question should be easier than I am making it out to be. again Im tired.

#3)A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is $91. How much is invested at 8%. THE ANSWER WAS= ($700)

I have not really worked with interests before, so maybe I am thinking too hard since it says the word interest.

I bet these are pretty easy to you guys :lol:

The good news is that this will be my last question for this test preparation. I appreciate your guys help thus far, and in advance.

Its just hard trying to hold a full time job, then studying all night long for preparation of a new one. I am about beat

YOU GUYS ARE SAVING ME HOURS OF RESEARCH. thank you, thank you, thank you

If your test is tomorrow, GO TO BED!!! You aren't going to learn all of this stuff at this point!

For #1....

If the boat goes 72 miles downstream in 3 hours, then its downstream rate is distance / time, or 72 / 3, or 24 miles per hour.

If the boat travels 60 miles in 6 hours going upstream, its upstream rate is 60 / 6, or 10 miles per hour.

Let x = speed of boat in still water
Let y = speed of current

Going downstream, the speed of the current is ADDED to the speed of the boat in still water, making the boat go faster. Going downstream,

x + y = 24

Going upstream, the speed of the current is SUBTRACTED from the speed of the boat in still water, making the boat go slower.

x - y = 10

Ok...

x + y = 24
x - y = 10

ADD the two equations together, and the y-terms will be eliminated:

2x = 34

x = 17

The speed of the boat in still water is 17 mph.

Now....can you take it from there?


#2....

let x = first number
then 17 - x = second number

The sum of the squares of these numbers is 145. So,

x<SUP>2</SUP> + (17 - x)<SUP>2</SUP> = 145

x<SUP>2</SUP> + 289 - 34x + x<SUP>2</SUP> = 145

Ok...in your ballpark now.

#3

You don't say, so I'll assume that the investment is for 1 year, and that this is simple interest....SUCH THINGS ARE IMPORTANT, and I hate to make assumptions!!

Let x = amount invested at 10%

Twice as much was invested at 8%, so
2x = amount invested at 8%

OK....simple interest formula follows:

Interest = principal * rate * time

x dollars invested at 10% for 1 year would earn this:

interest = x * .10 * 1

2x dollars invested at 8% for 1 year would earn this:

interest = 2x * .08 * 1

The total interest earned on the two investments is 91. So,

91 = x*.10 + 2x * .08

Again...take it from here.