Here's another problem I'm having a little trouble with:
A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized piece, and the shortest piece is 23 cm shorter than the longest piece. Find the lengths of the three pieces.
What could be an equation I could write?
Thank you so much!
Thank you very much!
Thanks!
whats the answer?
call the middle size m
then the long piece is 3 m
and the short piece is 3m-23
so
(3m-23) + m + 3m = 40
7 m -23 = 40
solve for m
How about:
let the shortest piece be x cm
<the shortest piece is 23 cm shorter than the longest piece> or
the longest piece is 23 more than the shortest piece,
so longest = x+23
<The longest piece is 3 times as long as the middle-sized piece> or
the middle piece is 1/3 of the longest piece,
so middle piece = 1/3(x+23)
then x + (x+23) + 1/3(x+23) = 40
(I get x=4, for the shortest piece of 4 cm)
7m - 23 =40
+ 23 +23
then 7m=63
then you divide 63 by 7 it equal 9
so the ans. is m=9 :)
To find the lengths of the three pieces, let's assign variables to represent the lengths.
Let's say:
- The length of the longest piece is L cm
- The length of the middle-sized piece is M cm
- The length of the shortest piece is S cm
The problem states that the longest piece is 3 times as long as the middle-sized piece, so we can write the equation: L = 3M.
It also states that the shortest piece is 23 cm shorter than the longest piece, so we can write another equation: S = L - 23.
We also know that the sum of the lengths of the three pieces is 40 cm, so we can write a third equation: L + M + S = 40.
Now we have a system of three equations:
1) L = 3M
2) S = L - 23
3) L + M + S = 40
You can solve this system of equations by substitution or elimination to find the lengths of the three pieces.