help hel p help

Question

The sum of three numbers is
115
. The third number is
4
times the first. The second number is
7
more than the first. What are the numbers?

Answer 1

Let x=first number

 

The sum of the three numbers = 115.

   First Number         +     Second Number     +     Third Number    =   115

         x                        +     (7+x)                          +       (4x)               =   115

Rewrite:

     x  +  (7+x) + (4x) = 115

     6x + 7 = 115                           [collect terms]

     6x = 108                              [subtract 7 from both sides]

     x = 18      [first number]

     x+7 = 25 [second number]

     4x = 72 [third number]

 

Check:

  Is 18 + 25 + 72 = 115  ?

        115 = 115   ? yes

Answer 2

Hello!

 

The second and the third number are described in relation to the first number. If you designate the first number with the variable X, the second number is 7 more than X (also written as X+7), and the third number is 4 times X (also written as 4*X, or just 4X). All three of these numbers added together should equal 115.

 

Added together, the equation is: 115 = X + X + 7 + 4X

 

Now solve for X, the first number:

 

115 = X + X + 7 + 4X (add the first two X's together to get 2X)

115 = 2X + 7 + 4X (then add 2X + 4X to get 6X)

115 = 6X + 7 (then subtract 7 from both sides)

108 = 6X (then divide 6 from both sides)

18 = X

 

Therefore 18 is your first number, 25 is your second number (18 + 7), and 72 is your third number (4 * 18).

 

You can check your answer by adding those three numbers together: 18 + 25 + 72 = 115

 

Answer 3

Let a = first number

Let b = the second number

Let c = the third number

 

Use these variables to set up equations.

 

a + b + c = 115                 eq1

 

c = 4a                             eq2

 

b = a + 7                         eq3

 

 

We have 3 equations with 3 different variables to work with.  This is what we call a system of equations.  What we need to do is get a single equation with only one variable, and solve for that variable.  Once you have that variable, we can solve for the others by substitution.

 

 

Substitute eq2 and eq3 into eq1. 

 

a + (a + 7) + 4a = 115       

 

 

Solve for a from this equation.

 

6a + 7 = 115

 

 

Subtract 7 on both sides of the equation.

 

6a = 108

 

 

Divide both sides of the equation by 6.

 

a = 18

 

 

Next, we substitute this value of a into eq2 to solve for c, and substitute that value of a into eq3 to solve for b.

 

c = 4(18)

c = 72

 

b = 18 + 7

b = 25

 

 

Our three numbers are 18, 25, and 72.

Answer 4

Let the first number be X then the second is X + 7 and the third would be 4X 

 

Since it's the  add all 3 of them and equate it to 115.

 

x + (X+7) + 4x = 115

 

6x = 108

 

x = 18

 

the numbers are 18, 25 & 72 those are your numbers .

 

regards,

 

MAYURAN