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Question

The sum of three numbers is 1032. Find the numbers, knowing that the second number is three times the first number and the third number is 60 more than half of the first number.

Answer 1

Given:   a + b + c = 1032

 

Given:   b = 3a

 

Given:   c = a/2 + 60

 

Substitute:  a + (3a) + (a/2 + 60) = 1032

 

Solve for a:

Combine like terms: 4a + a/2 + 60 = 1032

 

Subtract 60 from both sides:  4a + a/2 = 972

 

Multiply both sides by 2:  8a + a = 1944

 

Combine like terms:  9a = 1944

 

Divide both sides by 9:  a =  216

 

a= 216

 

b = 3 * 216 = 648

 

c = (216/2) + 60 = 168

 

PROVE:  216 + 648 + 168 = 1032

Answer 2

Hi Sarah,

 

 

Let the three numbers be x, y and z

 

The sum of three numbers=1032

 

 x+y+z=1032      equation 1

 

The second number is three times the first number

y=3x    equation 2

 

The third number is 60 more than half of the first number

z=60+(1/2)x    equation 3

 

substitute the values of y and z in equation 1

 

x+3x+60+(1/2)x=1032

   (9/2)x=1032-60

   (9/2)x=972

 

 x=(972)(2/9)

   

x=216

 

substitute the value of x in equation 2

 

y=3x

y=3(216)=648

 

substitute the value of x in equation 3

 

z=60+(1/2)x

z=60+(1/2)(216)

 =60+108

  =168

 

so the answer is x=216, y=648 and z=168