Directions on solving word problem. Answers are -11 and 44.?

Question

The difference between two numbers is 55. Four times the smaller number plus five times the larger number is 176. What are the numbers. -11 and 44. I know this is x + y = 55 and 3x + 5y=176. What do I do next?

Answer 1

x - y = 55 - - - - - - - - - Equation 1

4x + 5y = 176- - - - - - -Equation 2

- - - - - - - - - - - - - - - -

substitute Method Equation 1

x - y = 55

x - y + x = 55 - x

- y = 55 - x

- 1(- y = 55 - x)

y = - 55 + x

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - - -

4x + 5y = 176

4x + 5(-55 + x) = 176

4x + (-220 + 5x) = 176

4x - 220 + 5x = 176

4x - 220 + 5x + 220 = 176 + 220

9x = 396

9x/9 = 396/9

x = 44

The answer is x = 44

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - -

x - y = 55

44 - y = 55

44 - y- 44 = 55 - 44

- y = 11

- 1(- y = 11)

y = - 11

The answer is y = - 11

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

x - y = 55

44 - (- 11) = 55

44 + 11 = 55

55 = 55

- - - - - - - - - - - - - - - - - - - - - - -

Answer 2

It is actually x-y=55 and 4y+5x=176. You then need to get either x or y in the first equation on one side of the = sign. So x=55-y. Then you would substitute x in the second equation; 4y+5(55-y)=176. It then becomes 4y+275+5y=176. Then 9y+275=176. Subtract 275 from 176 and that equals -99. So then you have 9y=-99. Divide by 9 and y=-11. Then go back to the original equation. x-(-11)=55. It then becomes x+11=55. X=44, Y=(-11)

Answer 3

Let x= the first no.
y= the second no.

Given: x-y=55 (1)

Also given: 4y+5x=176. (2)

You ask: What do I do next?

My answer: First check your equations. Where did 3x come from? The difference between the two numbers is 55, not the sum. Sorry but your two equations won't give you the right solution.

Let's proceed:

From equation 1

x=55+y

Substitute this value in equation 2:

4y+5(55+y)=176

Simplify:

4y +275+5y=176
9y=176-275
9y=-99
y=-99/9
y=-11

Substitute this in equation 1:

x-(-11)=55
x+11=55
x=55-11
x=44.

Your answers are correct! But please study the above
solution. You won't get credit for correct answers if your
solution is wrong.

Answer 4

First you need to get your equations *correct*:
Let x be the smaller number
Let y be the bigger number

"The difference between two numbers (bigger minus smaller) is 55."
y - x = 55

"Four times the smaller number plus five times the larger number is 176."
4x + 5y = 176

So your two equations should be:
y - x = 55
4x + 5y = 176

Either solve it by substitution, or by adding the equations to eliminate a variable.

METHOD 1: SUBSTITUTION:

Original equation
y - x = 55

Solve for one variable (e.g. y)
y = x + 55

Now substitute this into the second equation:
4x + 5y = 176
4x + 5(x + 55) = 176

Distribute through:
4x + 5x + 275 = 176

Combine y terms on one side and numbers on the other:
9x = 176 - 275

Simplify:
9x = -99
x = -11

Now plug this back into the original equation to get x:
y - x = 55
y - (-11) = 55
x + 11 = 55
y = 55 - 11
y = 44

So your answers are -11 and 44


METHOD 2: COMBINING EQUATIONS:

Original equations:
y - x = 55
4x + 5y = 176

You want to eliminate a variable, so make one of the terms the same by multiplying.

For example, multiply the top equation by 5, so both equations have 5y in them:
5y - 5x = 275
4x + 5y = 176

I like ordering the terms the same way for the next step:
5y - 5x = 275
5y + 4x = 176

Now we need to subtract one from the other:
5y - 5y - 5x - 4x = 275 - 176

The 5y cancel out:
-9x = 99

Simplify:
x = -11

Again substitute x into one of the equations to get y.

y - x = 55
y - (-11) = 55
x + 11 = 55
y = 55 - 11
y = 44

Either method works, but the most important step is getting your equations correct at the beginning. And it is always good to check your answers.

44 - (-11) = 55, check
4*(-11) + 5*(44) = 176, check

So your answers are -11 and 44, like you said.

Answer 5

First off, your two equations are incorrect.

The difference between two numbers is 55:

x - y = 55

Four times the smaller number plus five times the larger number is 176:

4y + 5x = 176
(y must be the smaller number, due to the first equation above.)

Now, you need to combine these equations. First, multiply the first one through by 4 to get a common term between the two equations (4y):

4(x) - 4(y) = 4(55)
4x - 4y = 220

Now, add this to the second equation:

(4x - 4y) + (4y + 5x) = 220 + 176
9x = 396
x = 44

And plug this back into the first equation:

44 - y = 55
-y = 55 - 44
-y = 11
y = -11

Answer 6

x - y = 55

4x + 5y = 176


First, it is the *difference* between two variables. So x-y = 55 not x + y.

Also it is 4 times the smaller number, not 3 times.

NEXT, you need to do something so that you can get rid of one of the variables.

How about we multiply the first equation by -4

That way, x turns to -4x and will cancel with the 4x in the second equation.

-4x - 4y = -220
4x + 5y = 176

Add them:

y = -11

So, x - y = 55

x - (-11) = 55
x + 11 = 55

So x = 44

The numbers are -11 and 44 like you said.

Answer 7

You have the wrong equations, they should be:

x - y = 55
4y + 5x = 176.
From first equation:
x = y + 55
Substitute x in second equation and find y.
4y +5*(y+55) = 176

Answer 8

The first equation is actually y-x=55 because y is the bigger number and the difference is 55. The second equation is 4x+5y=176. So...

-x+y=55
4x+5y=176

If you multiply the top equation by 4 and add both equations you get:
4*(-x+y=55)............-4x+4y=220
4x+5y=176...........+ 4x+5y=176
----------------------------------------
......................................9y=396 so y=44 and x=-11

Plug in your numbers and they should match for both equations.

Answer 9

x+y=55 x+5y=176
The you need to eliminate one of the variables (x or y).
rewrite the 1st equation as

x= 55-y

then substitute into the second one,

55-y+5y=176

so

4y=121, y=121/4

then put this back in the original equation to find x,

x+121/4=55

x=99/4

so solution is (99/4, 121/4)

Answer 10

Suppose the smaller number is s.
Then the other one is s+55.
4s + 5(s+55) = 176
9s + 275 = 176
9s = 99
s = 11
The smaller one is 11. The larger one is 66

Th