Equation to solve '10-ft board cut into 3 pieces' type probs

[coloradocargirl]

I'd like to see what the actual equation is to solve this problem so I can use as a basis to create others like it. I can get halfway through and then get stuck. The answer is 2.75, I'm just not sure how to get to it. Thanks in advance!

A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4.5 ft. longer than the second. How long is the first piece?

 

[Deleted member 4993]

Re: Equation to solve these types of problems

I'd like to see what the actual equation is to solve this problem so I can use as a basis to create others like it. I can get halfway through and then get stuck. The answer is 2.75, I'm just not sure how to get to it. Thanks in advance!

A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4.5 ft. longer than the second. How long is the first piece?

Please show your work - showing exactly where you are stuck.

That way we know where to begin to help you.

 

[coloradocargirl]

Thanks!

Here's what I have, I just don't know exactly how to go any further or if I'm even correct in what I've done.

a=1st piece
b=2nd piece
c=3rd piece

a=2b
b=1/2a
c=b+4.5

a+b+c=10

2b+1/2a+(b+4.5)=10

 

[coloradocargirl]

Also, I didn't add the answer in the equation because I need to know how to get it. The only reason I know the answer is because the question is multiple choice and I have the answers (practice test).

 

[Denis]

a=1st piece
b=2nd piece
c=3rd piece
a=2b
b=1/2a
c=b+4.5
a+b+c=10
2b+1/2a+(b+4.5)=10

CARletta, always try for 1 variable if possible:
1st piece = a ; then:
2nd piece = a/2
3rd piece = a/2 + 4.5
So:
a + a/2 + a/2 + 4.5 = 10 ; multiply by 2:
2a + a + a + 9 = 20 : finish it