How will I figure this word problem out? The answers are 11 and 32.?

Question

The sum of two numbers is 43. One number plus three times the other number is 65. What are the numbers?

Answer 1

x + y = 43 - - - - - - - -Equation 1

x + 3y = 65 - - - - - - - Equation 2

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Substitute Method equation 1

x + y = 43

x + y - x = 43 - x

y = 43 - x

Insert the y value into equation 2

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Solving for x equation 2

x + 3y = 65

x + 3(43 -x) = 65

x + 129 - 3x = 65

- 2x + 129 - 129 = 65 - 129

- 2x = - 64

- 2x/-2 = - 64/ - 2

x = 32

The answer is x= 32

Insert the x value into equation 1

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Solving for y equation 1

x + y = 43


32 + y = 43

32 + y - 32 = 43 - 32

y = 11

The answer is y = 11

Insert the y value into equation 1
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Check for equation 1

x + y = 43

32 + 11 = 43

43 = 43

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Check for equation 2

x + 3y = 65

32 + 3(11) = 65

32 + 33 = 65

65 = 65

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The solution set is { 32, 11 }

Answer 2

Let x be one of the numbers, so that the other is 43 - x. Then, 3x + 43 -x = 65 => 2x = 22 => x =11. The other number is 43 -x = 43 - 11 = 32

Answer 3

you need two equations to solve this problem

x+y=43
x+3y=65

You have to solve this by canceling out the x's. Multiply the first equation by -1 and the second by 1.

(-1)x+y=43 -x-y=-43 2y=22 y=11

Now put 11 into the first equation and solve for x.

x+11=43 x=43-11 x=32
(1)x+3y=65 x+3y=65

Answer 4

x + y = 43 => x = 43 - y

x + 3y = 65=> 43 - y + 3y = 65 => 2y = 22

so y=11 and x = 43-11=32

Answer 5

Let x,y be the 2 nos. As per the statement, x+y=43;
and x+3y=65. Solving the 2 eq's, you will get x=32 & y=11.

Answer 6

32+ 3(11)
32+33=65

Answer 7

let the numbers b x and 43-x
x + 3(43-x) = 65
x + 129 - 3x=65
-2x=-64
x = -64/-2 = 32
the other number is 43-32=11

therefore, the nos. are 32 and 11

Answer 8

X is the first number.
Y is the second number.

The sum of two numbers is 43. (Sum means to add)
X + Y = 43

One number plus three times the other number is 65. (It doesn't matter if you use x + 3y or y + 3x)
X + 3Y = 65

Now either eliminate or substitute to solve for x and y.

Hope this helps. Good Luck.

Answer 9

let one no =x & other be= y
x+y=43 & x+3y=65
subtracting the values of the first equation from the second
x+3y=65
-{x+y=43}
2y=65-43
2y=22
y=22/2=11
from equation one x+y=43
x+11=43
x=43-11
x=32

Answer 10

First number = x
Second number = y

x + y = 43

One number (x) + 3 times the other number (3y) = 65

So:

x+y = 43 and
x + 3y = 65

Multiply your first equation by -1 so that the "x's" will cancel.

-x -y = - 43
x + 3y = 65

Add them together:

2y = 22

y = 11

If y = 11, then x will be 43 -11 = 32.

11 and 32, just like you said.

Regards,

Mysstere