word problems help?

Question

1. one number is 11 more than twice another number.If the sum of the numbers is twice their difference find the numbers.

i cant get this...help please

2. Mrs.West is 14 years younger than her aunt.If Mrs.West age in years is as much below 60 as her aunts age is over 40 how old is each

Answer 1

x is first number
y is second number

x=2y+11
x+y=2(x-y)=2x-2y
subtract x from both side and add 2y to both sides
y+2y=2x-x
3y=x Substituting into the first equation
3y=2y+11 subtracting 2y from both sides
y=11 which makes x=33

Checking the math 33 is 11 more than two times 11 YES
33+11 equals 2 times 33-11 YES

2) W is Mrs. West age
A is age of aunt
W+14=A
60-W=A-40 substituting the first into the secon
60-W=(W+14)-40
60-W=W+14-40 numbers on one side, W on the other
60-14+40=W+W
86=2W
W=43
A=57
checking to make sure
43 is 14 less than 57 YES
W is as much below 40 (-3) as A is above 60 (-3) YES

Answer 2

The above show how to work the problems once you know the equations. Just in case you can't figure out how to build them from the words, I thought I'd pipe in with that:

"one number" [ x ]
"is" [ = ]
"eleven more than" [ 11 + ]
"twice" [ 2 * ]
"another number." [ y ]
put it all together to get: x = 11 + 2y

"the sum of the numbers" [ x + y ]
"is" [ = ]
"twice" [ 2 * ]
"their difference" [ (x-y) ]

putting this together gives: x + y = 2 * (x-y)


Mrs West [ x ]
is [ = ]
14 years younger than [ -14 + ]
her aunt [ y ]
x = -14 + y
or
x = y - 14

Mrs West's age below 60 -> differnece between 60 and age
[60 - x]
is [ = ]
aunt's age [ y ]
over 40 [ - 40 ]

60-x = y-40

Answer 3

1. Set up a system of equations. Let x represent one number and y represent another.
First part:
x = 2y + 11
Second part:
2(x - y) = x + y

Plug the first equation into the second and solve:
2((2y + 11) - y) = 2y + 11 + y
2y + 22 = 3y + 11
y = 11

Plug this into the first equation:
x = 2(11) + 11
x = 33

So the two numbers are 33 and 11.



2. Same idea, let Mrs. West's age equal x, and her aunt's age equal y:

First part:
x = y - 14

Second:
60 - x = y - 40

Now, plug first eq. into second:
60 - (y - 14) = y - 40
74 - y = y - 40
2y = 114
y = 57

Plug this into first eq.:
x = 57 - 14
x = 43

So Mrs. West is 43 and her aunt is 57.

Answer 4

Let x = smaller number, y = the larger.

2x + 11 = y
2x = y - 11
x = 1/2y - 5.5

x + y = 2(y - x)
x + y = 2y - 2x
3x = y
x = 1/3y

1/2y - 5.5 = 1/3y
1/2y - 1/3y = 5.5
1/6y = 5.5
y = 33

x = 1/3(33)
x = 11

answer: x = 11, y = 33

Proofs:
33 is 11 more than twice 11
44 (33 + 11) is twice of 22 (33 -11)

The 2nd sentence of 2nd problem gibbers. It lacks the necessary conjunctions, etc. to be meaningful or of value.

Answer 5

x = 1st number
y = 2nd number
x = 2y+11
x+y = 2(x-y) --> x+y = 2x-2y -> x = 3y
3y = 2y+11
y= 11 = 2nd number
x = 2y+ 11 = 33 = 1st number

x = West's age
y = aunt's age
x = y-14
60- x = y - 40 --> x+y=100
y-14 +y = 100
2y= 114
y = 57 = aunt's age
x = y-14 = 43 = West's age

Answer 6

Two numbers are 11 and 33.
Mrs West age is 43 and her Aunt is 57 years..

Answer 7

1.Y = 11 + 2X . (Y + X) = 2(Y - X)
( 11 + 2X + X) = 2(11 +2X -X)
(11 + 3X) = 2( 11 + X)
(11 + 3X = (22 +2X)
3X -2X = 22 - 11
X = 11 Y = 33


2.W = A-14

60 -W =40 + A 60 - (A -14) = 40 -A

Answer 8

1. 33 and 11

2. 43 and 57

Answer 9

I will help:

1)

"One number" =x

This is because you don't know what it is.

"another number" = y

This is because it isn't necessarily x and you don't know what it is.

The sum of the numbers = (x+y)

is double their difference = +/-(2*(x-y))

find the numbers. You have 2 equations and 2 unknowns: solve it.

2)

Mrs. West's Age = x
Because we don't know what it is

Mrs. West's aunt's age = y
Because we don't know what it is and it might not be the same as Mrs. West's Age

60-x = y-40

Two equations and 2 unknowns solve it!

Answer 10

1.
The problem states two equations:
X=11+2Y
X+Y=2*(X-Y)

substituting 11+2y for x in the second equation gives:
(11+2*Y)+y=2*((11+2*Y)-Y)
11+3Y=2*(11+Y)
11+3Y=22+2Y
Y=11

Using the first equation we can now solve for x:
X=11+2Y
X=11+2*11
X=33

2.
X+14=Y
60-X=Y-40

60-X=(X+14)-40
60-X=X-26
2X=86
X=43

43+14=Y
Y=57