The sum of three numbers is 114. The third number is 4 timmes the second, The seconnd number is 6 morre than the first. What are thee numbers?

Question

I need help as soon as possible. Please Help me

Answer 1

Hi Daniel,

 

Let's begin by representing our 1st number as x.

Then our 2nd number is said to be 6 more than the 1st number, which we can represent as x + 6.

Lastly, our 3rd number is said to be 4 times the 2nd number, which we can represent as 4(x + 6).

 

Now can write our equation to express the sum of these three numbers as 114 and then solve for x to find the values of these three numbers:

    x + (x + 6) + 4(x + 6) = 114

    x + x + 6 + 4x + 24 = 114

    6x + 30 = 114

    6x = 114 - 30

    6x = 84

      x = 84/6 = 14 (1st number)

      x + 6 = 14 + 6 = 20 (2nd number)

      4(x + 6) = 4(20) = 80 (3rd number)

 

We can check our answers by adding these numbers up to see if their sum is 114:

     14 + 20 + 80 = 114

     34 + 80 = 114

     114 = 114

 

Their sum is 114, so we are confident that our three numbers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Let the first number = a

Let the second number = b

Let the third number = c

 

a + b+ c = 114

The question tells us that the third number is 4 x the second ( b);

however b = a+6

So we write the equation over to represent this

b =  6 more than a = a+6;

c= 4 x second = 4x (a+6)

New equation

a + (a+6)+ (4 x (a+6) = 114

 

Expand the bracket, Group similar

 

a+a+ 6 +4a+24 = 114

 

Put all unknown together (group) and all numbers together

 

a+a+ 4a = 114 - 6 - 24 ( the =6 and 24 becomes minus because when you move a number or unknown over the equal sign the number changes that is if it was positive it becomes negative -; if it was negative it become positive.

6a (a=a=4a) = 84 (114- 24-6)

6a = 84

a = 84/6 ( 6a = 6 x a; when we move it across the line it becomes the opposite; the opposite of multiply is divide)

a = 14

 

Substitute the answer 14 for "a" in original equation

b = 6 more than a = (14+6) = 20

C = 4 x the second number = 4 x 20 = 80

Substitute the numbers in equation

a+b+c = 114

 

14+20+80 =114

 

114 = 114