SOLUTION: I am having trouble with word problems: The question I have is: Divide 72 into three parts so that the first part is 3 less than the second part and the third part is 1/2 of the se

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Question 490747: I am having trouble with word problems: The question I have is: Divide 72 into three parts so that the first part is 3 less than the second part and the third part is 1/2 of the second part. I have no idea how to set up the formula and solve it.
Thank you,
Cindy
Found 3 solutions by lwsshak3, josmiceli, MathLover1:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I am having trouble with word problems: The question I have is: Divide 72 into three parts so that the first part is 3 less than the second part and the third part is 1/2 of the second part. I have no idea how to set up the formula and solve it.
**
let x=second part
x-3=first part
x/2=third part
..
all three parts total=72
x+x-3+x/2=72
LCD=2
2x+2x-6+x+144
5x=144+6=150
x=30
Ans:
first part=30-3=27
second part=30
third part=30/2=15

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The simple, direct way is to call the 3 parts
a, b, and c
given:
(1) +a+%2B+b+%2B+c+=+72+
(2) +a+=+b+-+3+
(3) +c+=+b%2F2+
-------------
Now substitute (2) and (3) into (1)
(1) +b+-+3+%2B+b+%2B+b%2F2+=+72+
Multiply both sides by 2
(1) +2b+-+6+%2B+2b+%2B+b+=+144+
(1) +5b+=+150+
(1) +b+=+30+
and, since
(2) +a+=+b+-+3+
(2) +a+=+30+-+3+
(2) +a+=+27+
and
(3) +c+=+b%2F2+
(3) +c+=+15+
The parts are 27, 30 and 15

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the first part be x,the second part is y, and the third part is z
given:
the first part is 3 less than the second part
x%2B3=y

the third part is 1%2F2 of the second part
z=y%2F2...or z=%28x%2B3%29%2F2
x%2By%2Bz=72
x%2B%28x%2B3%29%2B%28x%2B3%29%2F2=72.....solve for x
2x%2B3%2Bx%2F2%2B3%2F2=72
2.5x%2B4.5=72
2.5x=72-4.5
2.5x=67.5
x=67.5%2F2.5
highlight%28x=27%29...the first part
now find the second part
y=x%2B3
y=27%2B3
highlight%28y=30%29
and the third part

z=%28x%2B3%29%2F2
z=%2827%2B3%29%2F2
z=30%2F2
highlight%28z=15%29

check:

x%2By%2Bz=72
27%2B30%2B15=72
57%2B15=72
72=72