Forget the meaning of life--the real search is for the value of x!


Basic Algbebra:

A number has two digits.  When the two digits that make up the number are added, their sum is 15.
When the number is reversed ( for example 12 becomes 21), the new number is 9 more than the initial number.

What is the number?  Provide mathematical details of your answer.

cheers

A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

Solve this equation:

Solve: sqrt(x-4) + 10 = sqrt(x+4)

The answer to the first question is 78 and 87.

87-78=9

8+7 or 7+8 equals 15

Let x be the first digit and y the second digit of the first number. Thus the first number could be written xy.

Since this is a two digit number it is actually composed thus;

xy => 10x + y

When the digits are reversed, we get the number yx, which really translates to;

yx => 10y +x

The sum of the digits of the first number is 15, thus

x + y = 15 ------------------------------------------- (1)

The second number is 9 more than the first, thus

10x + y + 9 = 10y + x, which reduces to

x - y = -1 --------------------------------------------------- (2)

So we have two equations, (1) and (2)

From whence x = 7 and y = 8.

So the first number is 78.

QED

Excellent answer Huxley . . . i just couldnt figure out how to work with the "two digit number" information.

sqrt(x-4) + 10 = sqrt(x+4)

Square both sides;

(x-4) +20sqrt(x-4) +100 = (x+4)

20sqrt(x-4) = -92

x = (-92/20)^2 + 4

kobe:

A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

Let sisters age now = a
boy's age now = a - 3

3 yrs ago

Sisters age = a - 3
boy's age = (a - 3) - 3 = a - 6

therefore (a - 6) = 2/3(a - 3)

Solving equations for a . . . sister's age now = 12, brother's age now = 9.

kobe:

Solve this equation:

Solve: sqrt(x-4) + 10 = sqrt(x+4)

I expected the answer would be a round figure. Arrived at the same answer as Huxley . . .

4Him:

Excellent answer Huxley . . . i just couldnt figure out how to work with the "two digit number" information.

Thanks for the compliments. I remembers setting a similar problems to a class of students learning mathematical modelling some years ago.

Wow good job guys. you've certainly more than met expectations, way to go. I'll post more below.

Enjoy

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

A number P is divisible by 2, 3, and 15. Find a number P, such that P + 30 is also divisible by 2, 3, and 15.
Show your work.

Of the 6 courses offered by the music department at her college, Kay must choose exactly 2 of them. How many different combinations of 2 courses are possible for Kay if there are no restrictions on which 2 courses she can choose?

Let the function f be defined by f(x) = x² - 7x + 10 and f(t + 1) = 0, what is one possible value of t?

If the positive integer y leaves a remainder of 2 when divided by 8, what will the remainder be when y + 9 is divided by 8?

kobe:

If the positive integer y leaves a remainder of 2 when divided by 8, what will the remainder be when y + 9 is divided by 8?

y = 8n + 2

so, if we add 6 to y, it will make it a multiple of 8. So we are left with a 3.

So the remainder is 3.

kobe:

Let the function f be defined by f(x) = x² - 7x + 10 and f(t + 1) = 0, what is one possible value of t?

t = 4 or 1

(t+1)² -7(t+1) +10 = 0

t² - 5t + 4 = 0

(t-1)(t-4) = 0

whence t = 1
or t = 4

QED

kobe:

A number P is divisible by 2, 3, and 15. Find a number P, such that P + 30 is also divisible by 2, 3, and 15.
Show your work.

I don't think this one is very well defined. In fact, P can be any multiple of 30, thus

30, 60, 90, 120, ,

kobe:

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

this is tough . . . dont have a good background in statistics but i think the answer is 5/18

Anyone solved it yet?

kobe:

Of the 6 courses offered by the music department at her college, Kay must choose exactly 2 of them. How many different combinations of 2 courses are possible for Kay if there are no restrictions on which 2 courses she can choose?

i think this is 6 P 2 = 30

kobe:

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

let me try. There are 100 seniors each with three opportunities. that makes a total of 300 opportunities. same goes for the sophomores and juniors bring it to a total of 800 opportunities. So, probablity that a senior will be chosen is number of senior opportunities diviided by total number of opportunities. which is 300/800 or 3/8


i hope we r not doing your assignment for u

donchichi:

let me try. There are 100 seniors each with three opportunities. that makes a total of 300 opportunities. same goes for the sophomores and juniors bring it to a total of 800 opportunities. So, probablity that a senior will be chosen is number of senior opportunities diviided by total number of opportunities. which is 300/800 or 3/8

Your answer is the correct one.

kobe:

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

I think its 3/8, been a while though so I'm not sure. Since there are 100 seniors and each seniors name entered 3 times so thats 300 entries, 150 juniors entered twice thats another 300 entries then sopohomore's once that makes 800 entries in all, 300 of which are seniors. So probability will be 300/800 which will be 3/8.

4Him:

i think this is 6 P 2 = 30

should be 15.

woohoo, you guys are getting them all right.

How many liters of a 10% solution of acid should be added to 20 liters of a 60% solution of acid to obtain a 50% solution?

I have $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. How many dimes, and how many quarters, do I have?

For non-Americans, a dime is $0.10 and a quarter is $0.25.

I was able to balance a weightless beam, ten meters long, on a fulcrum by putting a 6 kg mass on one end, and an unknown mass on the other end. To balance this, I had to place the fulcrum 1.5 meters from the 6kg mass. What is the unknown mass?

Rasheed can mow his mother's lawn in 6 minutes. His brother Peter can mow it in 9 minutes. How long will it take them to do it together, if each has his own lawnmower.

The following is invalid, explain why.

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
2 = 1

kobe:

The following is invalid, explain why.

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
2 = 1

if we reverse the eqn from the start;

x = a
x+x = x+a
2x = x+a

Now referring to your equation at exactly

2a-2x = a+x-2x

if we substititute the value fro 2x on the RHS, we get

a+x-(x+a) which gives 0

the 2x in the equation is a not a single entity but a sum of two entities

I see what you're getting at but that's not qutie the problem.
The statement is a valid one.

donchichi:


if we reverse the eqn from the start;

x = a
x+x = x+a
2x = x+a

Now referring to your equation at exactly

2a-2x = a+x-2x

if we substititute the value fro 2x on the RHS, we get

a+x-(x+a) which gives 0

the 2x in the equation is a not a single entity but a sum of two entities