SOLUTION: the sum of three numbers is 45. one number is five more than the second number. it is also twice the third. find the numbers.

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Question 513518: the sum of three numbers is 45. one number is five more than the second number. it is also twice the third. find the numbers.
Found 2 solutions by Maths68, MathTherapy:
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let Numbers are x, y, z
x+y+z=45..............(1)
x=y+5
x-5=y
y=x-5.................(2)
x=2z
x/2=z
z=x/2..................(3)
Put the value of x from (2) and (3) to (1)
x+x-5+x/2=45
2x+x/2=45+5
2x+x/2=50
Multiply by 2 both sides
2*(2x+x/2)=50*2
4x+x=100
5x=100
5x/5=100/5
x=20
Put the value of x in (2) and (3)
y=x-5.................(2)
y=20-5
y=15
z=x/2..................(3)
z=20/2
z=10
So Numbers are 20, 15, 10

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Let 1st number be F
Then second = F – 5
Also, third = ½F

We then have: F + F – 5 + ½F = 45
2½F – 5 = 45
2½F = 45 + 5
2½F = 50
5F/2 = 50
5F = 100 ----- Cross-multiplying
F, or 1st number = 100/5, or highlight_green%2820%29

2nd number = F – 5, or 20 – 5, or highlight_green%2815%29

3rd number = ½F, or ½(20), or highlight_green%2810%29

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Check
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First + second + third = 45

20 + 15 + 10 = 45

45 = 45 (TRUE)

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