Need help with some math questions

[GeordieMagpie]

'Ello folks, I recently crossed some questions and..I can't find a place more reliable than home!

So let's begin,

John has nickels, dimes and quarters, He has a total of 17.65$, he has eleven fewer quarter than nickels and six times as many dimes as quarters, how much of each coins does he have.
(nickel=5 cents dime=10 quarter=25)

An antique desk is 25 year older than an antique chair, in 15 years the desk will be twice as old as the chair, find the present age of the furniture

A test has 20 questions worth 100 points, the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each, how many multiple-choice questions are there.



At present, Michael is 4 years older than George, if Michael was 1 year younger, his age would be double George's age. Make two equations to find the age of Michael 3 years from now (all use Algebra one way or another I believe)

2 more (last ones, promise)

the product of two consecutive integers is 156, find the integers.


When the square of a number is added to the number tripled, the result is 108, what's the number?


THANK YOU

[Waltzinblack]

Desk is 35 years old, chair is 10.

Michael is 7, George is 3.

Got bored doing the money one.

[Deleted]

A test has 20 questions worth 100 points, the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each, how many multiple-choice questions are there.

7 Multiple choice worth of 77 points
11 True/flase worth 33 points
total of 100 points

DAMN WONG aah impossible!
Guys mine answer is wrong

[Deleted]

a = amount of nickles
b = amount of dimes
c = amount of quarters
n = nickle = 5 cents
d = dime = 10 cents
q = quarter = 25 cents

a*n + b*d + c*q = 1765 cents

a = c+11
b = 6*c

-> (c+11)*n + 6*c*d + c*q = 1765 cents

c*n + 11*n + 6*c*d + c*q = 1765

c(n + 6*d + q) + 11*n = 1765

c(n + 6*d + q) = 1765 - 11*n = 1765 - 11*5 = 1710

c = 1710/(n + 6*d + q) = 1710/(5 + 6*10 + 25) = 1710/90 = 19

So you have 19 quarters. Put the c = 19 back into

a = c+11
b = 6*c

And you get a = 30 and b = 114. Done.

Disclaimer: I can be wrong.

Cba with the second.

[Waltzinblack]

7 Multiple choice worth of 77 points
11 True/flase worth 33 points
total of 100 points

7 + 11 = 18, there are 20 questions.

Damnit, you changed the post just as I quoted it.

5 multiple choice questions, 15 true/false questions.

(5x11)+(15x3)=55+45=100

[Deleted]

Q2
chair = x
desk = x + 25

2(x + 15) = x + 40
2x + 30 = x + 40
x = 10

chair = 10 years
desk = 35 years

Q3
true/false = 3
true/false amount = t

mutichoice = 11
multichoice amount = m

3t + 11m = 100 (E1)

t + m = 20 (Multiply by 3)
3t + 3m = 60 (Take this away from E1)

8m = 40
m = 5

Q4
George = x
Michael = x + 4

2x + 1 = x + 4
2x = x + 3
x = 3

George = 3
Michael = 7

7 + 3 = 10

-

I could be wrong!

[Deleted]

<snip> due to cocky, incorrect reply.

[Deleted]

Glad I can still contribute. Most questions have gotten correct answers by now, except:

M=G+4
M-1=2G
G+4-1=2G
G=3

G+3=6

G is 6 (mind the 3 years from now)

Isn't it Michael's age in 3 years time that is being asked?

[KevyB]

nickels, dimes... jesus christ no wonder you people have trouble with maths, extremely inefficient numbering.

[Deleted]

Isn't it Michael's age in 3 years time that is being asked?

Got me. My mistake.

[Porcell]

'Ello folks, I recently crossed some questions and..I can't find a place more reliable than home!

So let's begin,

John has nickels, dimes and quarters, He has a total of 17.65$, he has eleven fewer quarter than nickels and six times as many dimes as quarters, how much of each coins does he have.
(nickel=5 cents dime=10 quarter=25)

An antique desk is 25 year older than an antique chair, in 15 years the desk will be twice as old as the chair, find the present age of the furniture

A test has 20 questions worth 100 points, the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each, how many multiple-choice questions are there.

At present, Michael is 4 years older than George, if Michael was 1 year younger, his age would be double George's age. Make two equations to find the age of Michael 3 years from now (all use Algebra one way or another I believe)

These are all "system of equation" questions.

5*n + 10*d + 25*q = 1765 [equation 1]
n-11=q [equation 2]
6*q = d [equation 3]

You have 3 variables and 3 equations, so you know you can solve it. Substitute variables into the first equation until you get one equation with one variable.
5*n + 10*(6*q) + 25*(n-11) = 1765
5*n + 10*(6*(n-11)) + 25*(n-11) = 1765 [This equation has just one variable, so you can distribute the multiplication, combine terms, and solve for n)

----------

The other questions are the same type of setup. Write out the equations that they describe, then solve for one variable. Once you have one variable known, you can plug that number back into the other equations and solve for the others:

Second Problem:
d = c+25
d+15 = 2*x

Third Problem:
t + m = 20
3*t + 11*m = 100

Fourth Problem:
g+4 = m
m-1 = 2g


----------

I shouldn't need to give you the answers, the above equations should be enough for you to figure them out.

[v2prwsmb45yhuq3wj23vpjk]

Since nobody else has seemed to have gotten the coin one, here you go:


x = quarters
y = nickels
z = dimes

Since there are 11 fewer quarters than nickels, we can conclude:

y = x + 11

Since there are 6 times as many dimes as quarters, we can conclude:

z = 6x

The equation would look like this:

25x + 5y + 10z = 1765

Divided by 5 it looks like:

5x + y + 2z = 353

Now, we plug in the stuff we figured out earlier, starting with the z:

5x + y + 2(6x) = 353 OR 17x + y = 353
Plugging in the y: 17x + x + 11 = 353 OR 18x = 342
Which means that: x = 19

Now that we know one variable, the rest becomes easy. y = 19 + 11 or y = 30, z = 6*19 or z = 114

Which means 114 dimes, 30 nickels, and 19 quarters.

[Porcell]

Since nobody else has seemed to have gotten the coin one, here you go:.

The fourth post has the answer...

[v2prwsmb45yhuq3wj23vpjk]

The fourth post has the answer...

I skipped to the bottom and saw that they said they could be wrong, thought that meant that they screwed up and they WERE wrong. Oh well, whatever.

[Deleted]

You should probably do this yourself. But I love algebra:

x*y=156
x+1=y

x*(x+1)=156
x²+x=156
x²+x-156=0
(x+13)(x-12)=0
x=-13 v x=12

probably x=12 and y=13 (not sure what defines an 'integer')

x²+3x=108
x²+3x-108=0
(x+12)(x-9)=0
x=-12 v x=9

probably x=9

[Julian Rayne]

I
let the number of quarters be x : Total value = 25x cents
number of nickels = x + 11 : Total value = 5(x + 11) = 5x +55 cents
number of dimes = 6x : Total value = 10*6x = 60x cents.

Total value = $17.65 = 1765 cents
Therefore 25x + 5x + 55 + 60x = 1765
Therefore 90x = 1765 - 55 = 1710
Therefore x = 1710/90 = 19

quarters = x = 19
nickels = x + 11 = 30
dimes = 6x = 114
Therefore he had 19 quarters, 30 nickels and 114 dimes.

II
Let the chair be x years old
The antique desk is 25 +x

In 15 years the chair is x + 15 years old
in 15 years the desk is 25 + x + 15 = x + 40 years old
the desk will be twice as old as the chair
Therefore x + 40 = 2(x + 15)
Therefore x = 40 = 2x + 30
Therefore 2x - x = 40 - 30
Therefore x = 10 = Age of chair
Therefore x + 25 = 35 = Age of Desk

The chair is 10 years old and the desk is 35 years old.

III
Let the number of T/F questions be x worth a total of 3x points
Therefore the number of MC questions will be (20 - x) worth a total of 11*(20 - x) points.

Total value = 100 points
Therefore 3x + 11*(20 - x) = 100
Therefore 3x + 220 - 11x = 100
Therefore -8x = 100 - 220 = -120
Therefore x = -120/-8 = 15
Therefore 20 - x = 5

There are 15 T/F questions and 5 MC questions.

IV
I find the language in this question ambiguous but I'll give it a try.

Let George be x years old
Let Michael's age be y years old
if Michel were 1 year younger he'd be y- 1 years old
He would be double George's age
Therefore y - 1 = 2x ----- Equation 1
Michael is 4 years older that George
Therefore y = x + 4-----Equation 2

Substitute the value of y from Equation 2 in Equation 1
x + 4 - 1 = 2x
Therefore x + 3 = 2x
Therefore x - 2x = -3
Therefore -x = -3
Therefore x = 3

Substitute the value of x in Equation 2
y = 3 + 4 = 7

3 years from now Michael will be y + 3 years old = 7 + 3 = 10 years old.

Michael's age will be 10 years old.

V
Let the two consecutive integers be x and x + 1
Their product is 156
Therefore x(x + 1) = 156
Therefore x^2 + x - 156 = 0
Therefore x^2 + 13x -12x - 156 = 0
Therefore x(x + 13) - 12 (x + 13) = 0
Therefore (x + 13)(x - 12) = 0
Therefore Either x + 13 = 0 OR x - 12 = 0
Therefore Either x = -13 OR x = 12

The number are EITHER 12 and 13 OR -13 and -12.

VI
Let the number be x
The square of the number is x^2
triple the number is 3x
The total is 108
Therefore x^2 + 3x = 108
Therefore x^2 + 3x - 108 = 0
Therefore x^2 + 12x - 9x -108 = 0
Therefore x(x + 12) - 9(x + 12) = 0
Therefore (x + 12)(x - 9) = 0
Therefore EITHER x + 12 = 0 OR x - 9 = 0
Therefore EITHER x = -12 OR x = 9

The number is EITHER 9 OR -12.