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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.
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2 Answers

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
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