Question

Three multiplied by the sum of 4 and a number is the same as 18 more than the number. Find the number.

If n is "the number," which equation could be used to solve for the number?


3n + 4 = n + 18
4(3 + n) =n + 18
3(4 + n) =n + 18
3(4 + n) + 18 > n

Answer 1

Can someone explain how to do this @Hero

Answer 2

The sum of 4 and a number is 4 + n
Three times that is 3(4 + n)
18 more than a number is n + 18

3(4 + n) = n + 18

Answer 3

But...wouldnt P.E.M.D.A.S apply here? so wouldnt it in fact be...wait...so...
The part that states:
Three multiplied by the sum of 4 and a number
means that 4+n is acctualy (4+n)? so it is realy 3(4+n)=18+n

Answer 4

PEMDAS only applies to simplifying numerical expressions. It doesn't apply to solving algebraic equations. When solving algebraic equations, you have to focus on isolating a variable..NOT PEMDAS.

Answer 5

>_> so...The lesson is called two or more unknowns...so...I have to follow the order its listed in the sentence?

Answer 6

Ok...That kind of makes sense hero....Can you watch me work out one more and assist me if im wrong?

Answer 7

Three-sevenths of a number is 21. Find the number. is the problem...

Answer 8

So...If its 3 parts of the number already...

Answer 9

If you were solving for n, you have to isolate n.

Answer 10

then i need to 21 and muliply it by 4 since it is already 3 parts of 7? and to get it to the full value id need to just multiply it by 4?

Answer 11

\[\frac{3}{7}n = 21\]

Answer 12

Ok...so instead of what ever i just attempted to say i need to take 21. divide it by 3. mulitply what i get from that by 7 and ill get n?

Answer 13

of means "times" or "multiply"

Answer 14

three-sevenths of a number means the same thing as three-sevenths TIMES the number.

Answer 15

? so i couldnt divide 21 by 3 and mutiply the awnser from that by 7? wouldnt it give me the same thing?

Answer 16

\[21 \div 3 = 7 \times 7 = 49\]

Answer 17

Yes, you can do that. If the number on the right is divisible by the numerator, then that would be a smart way to reduce the number on the right.

Answer 18

Hrmm...Could you tutor me? xD

Answer 19

Tutor you? Just post your questions on OS. You're already being tutored...sort of.

Answer 20

Ok...Well...These right here kind of...to be honest...they f--k with my head...like seriously...they make me rage...
Separate 846 into 3 parts so that the second part is twice the first part and the third part is triple the second part.

Which of the following equations could be used to solve the problem?


846 = x + 2x + 3x
846 = x + 2x + 6x
846 ÷ 3 = x + 2x + 6x
846 ÷ 3 = x + 2x + 3x

Answer 21

Just do each part one at a time. Start with the smallest part and then build to the largest part.

Answer 22

so...the 2nd one?

Answer 23

The first part is the smallest part, so label it x
The second part is twice the first part so 2x
The third part is triple the second part so 3(2x) or 6x

All three parts combined is equal to 846:
x + 2x + 6x = 846

Answer 24

So it is the 2nd one :D

Answer 25

Ok last one hero...i want to be SURE i got this down pat.

Five times a number is the same as 30 more than 8 times the number. Find the number.

Answer 26

so 5 = 30+8Xn

Answer 27

no wait i meant \[5 \times N = 30 + 8 \times n\]

Answer 28

Try to avoid using the times symbol when setting up algebraic equations. Simply write

\(5n = 30 + 8n\)

Make sure your variables match. For example, \(N\) is not the same as \(n\)

Answer 29

Ok. Understood. So...How would i solve for n? this is where i get confused...

Answer 30

Ever heard of like terms? Put like terms on the same side.

Answer 31

Isn't 8n and 5n like terms?

Answer 32

Ok...So let me try please...

Answer 33

The put the other terms (that are not like) on the other side.

Answer 34

8N can be subtracted from both sides so the new problem would be

Answer 35

\[-5N =30\]

Answer 36

Well...let me say something about that.

Answer 37

Ok

Answer 38

What you want to do is make sure that the number that is multiplied by the variable is positive.

Answer 39

Well...Wouldnt the next step be 30/-5N? so wouldnt that make it 6N?

Answer 40

so N=6?

Answer 41

\(5n = 30 + 8n\)

So subtract \(5n\) from both sides:
\(0 = 30 + 8n - 5n\)

Answer 42

Now...factor out the n:
\(0 = 30 + (8 - 5)n\)

Answer 43

Now obviously 8 - 5 = 3 so:
\(0 = 30 + 3n\)

Answer 44

Subtract 30 from both sides:
\(-30 = 3n\)

Answer 45

so..30/3N= 10=N

Answer 46

Now we can divide by a positive number:
\(-\dfrac{30}{3} = n\)

Remember to keep track of the negative and never divide by the variable.

Answer 47

\(-10 = n\)

Answer 48

-10?

Answer 49

Are you surprised?

Answer 50

Yea....a little bit...i thought that...It just...what?

Answer 51

They didn't say the number must be positive. Negative numbers are still numbers.

Answer 52

True...but...???? im trying to figure out how the 10 became negative...

Answer 53

i see where it became negative but why would it have to be subtracted...couldnt you flip it to the other side flipping its sign?

Answer 54

Sorry...i understand how you

Answer 55

did it...thats just the way my teachers taught me...

Answer 56

Because you want to divide only by positive numbers. Dividing by positive numbers make more sense than dividing by negative numbers.

Answer 57

>_> but...OH so...ok i still use the "house" sign for dividing because im a two year old inside...so...the positive number would be on the porch and the negative is under the roof? so...your not dividing by a negative number...the negative is being divided!!!