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# Help me with this problem!

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.

### 2 Answers by Expert Tutors

CHERYL S. | Math for all ages; K-8 All Subjects; Algebra; Geometry; SAT/ACT PrepMath for all ages; K-8 All Subjects; Alg...
4.9 4.9 (110 lesson ratings) (110)
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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
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
5.0 5.0 (240 lesson ratings) (240)
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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