coolawesomeryan
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Quick Math Question for 50 Points! Anybody willing to help? If so, brainliest plus huge thanks! :D
Eight less than the product of three and a number is the same as Four times the sum of the same number and two.
I need the steps, and for the final answer, I would like to know what n is.
Thank you for your help! Tremendously appreciated! :D

Sagot :

rvkacademic

Answer:

n = -16

Step-by-step explanation:

Best way to deal with these tricky word problems is to break it down into pats and convert each part to an algebraic expression. And man, do they make it tough :)

Look for the word number and the phrases relating to it. That is a starting point

Let's use n to represent the number

I will highlight each phrase as we go along

1. Eight less than the product of three and a number is the same as Four times the sum of the same number and two.
⇒  3n

2. Eight less than the product of three and a number is the same as Four times the sum of the same number and two.
⇒ 3n - 8

3.  is the same as ⇒  =

4. Four times the sum of the same number and two
sum of same number and 2 ⇒ n + 2

5. Four times the sum of the same number and two
⇒ 4(n + 2)

So we get the expression
3n - 8 = 4(n + 2)

To solve, first expand the brackets for the expression on the right
4(n + 2) ⇒ 4 x n + 4 x 2 = 4n + 8

⇒  3n - 8 = 4n + 8

Add 8 on both sides

⇒ 3n - 8 + 8 = 4n + 8 + 8

⇒ 3n = 4n + 16

Subtract 4n on both sides
3n - 4n = 3n - 3n + 16

⇒ -n = 16

So, n = -16

semsee45

Answer:

3n - 8 = 4(n + 2)

n = -16

Step-by-step explanation:

Define the variable

  • Let n be the unknown number.

Given:

  • Eight less than the product of three and a number is the same as Four times the sum of the same number and two.

Product is the result of multiplication.

Therefore, the "product of three and a number" is:  

  • 3n

Less than means to subtract.

Therefore, "eight less than the product of three and a number" is:

  • 3n - 8

The same as means equals.

Therefore, "eight less than the product of three and a number is the same as" is:

  • 3n - 8 =

Sum means to add.

Therefore, the "sum of the same number and two" is:

  • n + 2

Times means to multiply.

Therefore, the "four times the sum of the same number and two" is:

  • 4(n + 2)

Finally, "Eight less than the product of three and a number is the same as Four times the sum of the same number and two" is:

  • 3n - 8 = 4(n + 2)

Solving for n

Expand the brackets:

⇒ 3n - 8 = 4n + 8

Subtract 8 from both sides:

⇒ 3n - 8 - 8 = 4n + 8 - 8

⇒ 3n - 16 = 4n

Subtract 3n from both sides:

⇒ 3n - 16 - 3n = 4n - 3n

⇒ -16 = n

Therefore:

⇒ n = -16

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