Elementary Algebra problem solving strategy

Question

One number is three more than twice another their sum is -5

Answer 1

Hi Laura, thanks for your question! We can solve with the simple steps below. Let's assume we're using variables x and y.

1. Write Equation 1: Using the comment "their sum is -5", this tells us that: x+y=-5
2. Write Equation 2: Using the comment "One number is three more than twice another" this tells us that x is three more than double y. This can be written as: x=2y+3.
3. Isolate: Using "x+y=-5", isolate x: x=-5-y
4. Note: You can also isolate y and you will ultimately get the same result, but I've isolated x here for simplicity's sake!
5. Equate: Set Step 4 equation "x=-5-y" equal to Step 3 equation "x=2y+3" to yield: 2y+3=-5-y
6. Solve y: 2y+3=-5-y-->3y+3=-5-->3y=-8
7. y=-8/3
8. Solve x: Plug back in to solve x using "x+y=-5": x+-8/3=-5-->x=-5+8/3
9. x=-7/3

Answers:

1. x: -7/3
2. y: -8/3

Answer 2

Let the two numbers be x and y

x + y = -5

But x = 2y +3

Since x = 2y +3, let's rewrite x+ y = -5 like this:

2y +3 +y = -5

Let's collect like terms by grouping the all the Ys together:

2y +y +3 = -5

3y +3 = -5

now let's subtract 3 from both sides

3y +3 -3 = -5 - 3

3y + 0 = -8

3y = -8

Now we divide both sides by 3

3y/3 = -8/3

y = -2 2/3

Now that we know y = -2 2/3

let's go back to our original equation : X +Y = -5

let's plug in our answer for y in the original equation

X + (-2 2/3) = -5

X - 2 2/3 = -5

let's add 2 2/3 to both sides

X - 2 2/3 + 2 2/3 = -5 + 2 2/3

X + 0 = - 2 1/3

X = -2 1/3

Hope this explanation helps.

Answer 3

Assuming that the problem asks you to determine the two numbers.

Let's call the two numbers x and y. Their sum is -5, so x + y = -5

We also know that one number is 3 more than twice the other. Twice a number is multiplying it by 2. Three more than that is 2y + 3. That means that x = 2y + 3.

Now can substitute x from the 2nd equation into the 1st, yielding 2y + 3 + y = -5.

Combine like terms: 3y + 3 = -5; subtract 3 from both sides; 3y = -8; divide both sides by 3.

y = -8/3 or -2 2/3. Then x = -5 - (-2 2/3) = -2 1/3. Could also do x = 2(-2 2/3) + 3, or -5 1/3 + 3 = -2 1/3

Answer 4

So we are looking for two numbers: let’s say one number is “x” and the other number is “y”

we know their sum is 5, so

x+ y = 5

we know that one is 3 more (plus 3) than twice the number (2X). so

y= 3 + 2x

solve the first equation for x:

x = 5 - y

substitute (or “plug in”) this equation for x into the second equation:

y = 3 + 2*(5 - y)

solve for y, then substitute back into the x = 5 - y equation to solve for x.

I hope this explanation helps. I don’t solve the entire problem because I don’t want to just give answers. If you have more questions or would like to schedule a Tutor session, I am

offering a discount since I am new to the platform. Please let me know if you need more help!

Answer 5

n and 2n + 3

n + 2n + 3 = 5

Can you solve for n and answer?