Twice a number decreased by 8 is equal to the number increased by 10. Find the number

Question

I don't understand how to problems like this

Answer 1

Hello Teshawn,

Not every problem can be directly translated like this one, but I will line everything up to see how it goes.

 

Let 'x' be the number for which we are looking.

 

(Twice a number) (decreased by) (8) (is equal to) (the number) (increased by) (10)

         2x                       -              8          =                 x                   +            10.

 

So, we have:

2x - 8 = x +10

--> x = 18, by subtracting 'x' from both sides, and adding 8 to both sides.

Answer 2

Hey Teshawn,

Problems like this are usually best solved by translating the sentence they give you into an equation. We can take it step by step.

"Twice a number..."
'Twice' just means double or times 2. Anytime 'a number' or 'what number' or the like is used, that's where you put 'X'

 

"decreased by 8..."

Pretty straight forward. This just means 'minus 8'

 

"is equal to..."

Obviously the equals sign, though sometimes a problem may just say "is" or something similar.

"the number increased by 10."

Since it says 'the number' we have to use 'X' again. Increased by 10 means 'plus 10'

Put it all together: 2x - 8 = x + 10

 

From there, you just need to use algebra to solve for x.

2x - 8 = x + 10

- x       - x

x - 8 = 10

  + 8   + 8

x = 18

 

 

There are a few other tricks to make note of, like "percent" meaning "divided by 100" or 'of' typically meaning 'multiply.

 

Hope this helps!

Answer 3

We can set up an equation to solve this problem.  Anytime you see the phrase "a number" that represents our variable.  Let's use x for our variable.  You could replace x in the word problem anytime you see the phrase "a number."

 

So now we get:

 

Twice x decreased by 8 is equal to x increased by 10.

 

So if we find twice x that means we double it.  How do you double something?  Multiply it by two, so we get 2x.  8 less than 2x is 2x - 8.

 

The left side of our equation is 2x - 8.

 

x increased by ten is x + 10.

 

The right side of our equation is x + 10.

 

The left and right side are equal to each other so we get the equation is:

 

2x - 8 = x + 10

 

Now let's solve by getting x by itself on one side of the equation.

 

2x - 8 = x + 10  subtract x from each side

 

x - 8 = 10     add 8 to each side

 

x = 18

 

Let's check that our number for x is correct.  

 

2x - 8 = x + 10    if x = 18

 

2(18) - 8 = 18 + 10

 

36 - 8 = 18 + 10

 

28 = 28

 

We know that x = 18 is the correct answer.

 

Thanks for your question.

Tyler