ALGEBRA 2 help!!!! i have word problems!?

Question

please show me how to set up these equations and solve them show work if you can please!!!


the sum of two numbers is 161. two times the smaller number plus forty-seven is the larger number. what are the numbers???


the sum of a number and a number is that is two-thirds of the first number is fifty. what are the numbers?

the sum of two numbers is 2173.7 their difference is 884.1 what are the numbers?

SHOW WORK IF U CAN PLEASE!

Answer 1

Algebra 1 just teaches you how to solve word problems by assigning x as the unknown. Algebra 2 is a little bit tougher. Many times you have to deal with more than 1 variable. So here goes......

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The sum of two numbers is 161. two times the smaller number plus forty-seven is the larger number. what are the numbers?

Let
x = the smaller number
Here, never bother to solve for what to assign the larger number.
Let
y = the larger number

The sum of 2 numbers is 161
x + y = 161

two times the smaller number plus forty-seven is the larger number.
2 · x + 47 = y

Now we have the equations
x + y = 161
2x + 47 = y

How do you solve 2 equations with 2 variables? There are many methods of solving. But in this case I will show to you the quickest and most effective ways to answer.

We are given
2x + 47 = y
then,
y = 2x + 47

But
x + y = 161, so substitute y:
x + (2x + 47) = 161
x + 2x + 47 = 161
x + 2x = 161 - 47
3x = 114
x = 114/3
x = 38

We now have the value of x. To solve for y, substitute x = 38 to
y = 2x + 47
y = 2(38) + 47
y = 76 + 47
y = 123

Therefore,
the numbers are 38 and 123.

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The sum of a number and a number is that is two-thirds of the first number is fifty. what are the numbers?

Let
x = the first number
y = the number that is two-thirds of the first number

Thus,
To get the equations, analyze every part of the question.

Since their sum is 50,
x + y = 50

Since y is 2/3's x,
y = 2/3 x

We now have the equations
x + y = 50
y = 2/3 x

Now you can simply substitute y into the first equation
x + y = 50
x + (2/3 x) = 50
x + 2/3 x = 50

Multiply 3 to both sides
3x + 2x = 150
5x = 150
x = 150/3
x = 30

To solve for the other number, subs. x = 30 into
y = 2/3 x
y = 2/3 (30)
y = 20

Therefore, the numbers are 30 and 20.

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The sum of two numbers is 2173.7 their difference is 884.1 what are the numbers?

Let
x and y = the numbers

The question tells us that
x + y = 2173.7 and
x - y = 884.1

Here, if you add the two equations vertically, it yields
2x + 0 = 3057.8
2x = 3057.8
x = 3057.8/2
x = 1528.9

To solve for y,
x + y = 2173.7
y = 2173.7 - x
y = 2173.7 - 1528.9
y = 644.8

Therefore, the numbers are 1528.9 and 644.8.

Hope this helps^_^
^_^

Answer 2

1)
x is the small number
y is the larger number

the sum of two numbers is 161 -----> x + y = 161

two times the smaller number plus forty-seven is the larger number -----> 2x + 47 = y
Rewrite as : 2x - y = -47

Write them side by side and add the equations together:

x + y = 161
2x - y = -47

(x + 2x ) + (y - y) = (161 - 47)
3x + 0 = 114
3x = 114
x = 114/3
x = 38

x + y = 161 ---> 38 + y = 161

y = 123

2)
the sum of a number and a number is that is two-thirds of the first number is fifty

x is first number
y is second number

y = (2/3)x

x + y = 50

Try from there...


3)
the sum of two numbers is 2173.7

x + y = 2173.7

difference is 884.1

x - y = 884.1

Answer 3

the sum of two numbers is 161. two times the smaller number plus forty-seven is the larger number. what are the numbers???
x+y=161 2x+47=y
x+(2x+47)=161
3x+47=161
3x=114
x=38
2(38)+47=y
123=y

the sum of a number and a number is that is two-thirds of the first number is fifty. what are the numbers?
x+(2/3)x=50
1(1/3)x=50
x=30 the other number is 20

the sum of two numbers is 2173.7 their difference is 884.1 what are the numbers?
x+y=2173.7 x-y=884.1
x=884.1+y
(884.1+y)+y=2173.7
884.1+2y=2173.7
2y=1289.6
y=644.8 x=884.1+644.8
x=1528.9

Answer 4

The first one:
x+y=161
2x+47=y
This forms a system of equations. Just plug the second equation into the first one:
x+2x+47=161
and solve:
3x+47=161
3x=114
x=38
Go back to the first equation:
38+y=161
y=123

Number 2
Okay, this one doesn't make any sense to me.

Number 3:
x+y=2173.7
x-y=884.1
are the two equations that make up a system.
Change the second equation to x=884.1+y by adding y to both sides of the equation.
Then plug it into the first equation:
884.1+y+y=2173.7
884.1+2y=2173.7
2y=1289.6
y=644.8
So x=1528.9

Answer 5

x + y = 161
2x + 47 = y
substitute
x + (2x + 47) = 161
3x + 47 = 161
3x = 114
x = 38
therefore
y = 123


x + (2/3x) = 50
5/3 x = 50
x = 30
therefore
y = 20




x + y = 2173.7
x - y = 884.1

add...
2x = 3057.8
x = 1528.9
therefore
y = 644.8

Answer 6

x+y=161 2x+47=y
x+(2x+47)=161
3x+47=161
3x=114
x=38
2(38)+47=y
123=y

x+(2/3)x=50
1(1/3)x=50
x=30 the other number is 20

x+y=2173.7 x-y=884.1
x=884.1+y
(884.1+y)+y=2173.7
884.1+2y=2173.7
2y=1289.6
y=644.8 x=884.1+644.8
x=1528.9

Answer 7

this is the equation to the first

x+y=161

2x+47=y

just solve the system

Answer 8

well....since evry1 else has done it me doing it is really pointless. Just think of IS as = and SUM as + and OF as x. its really not too hard.

Answer 9

Do Your homework , by your own self ...