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Question 1017802: A stick 46 metres long is divided into two parts so that 2/5 of one part is equal to 3/4 of the other part. Find the lengths of the two pieces. [ Let the length of one part be x m, then the other length is (46-x)m] I've been struggling with this for more than 20 minutes, so I'm just wondering if you could help, thank you.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let one part be equal to x and let the other part be equal to y.
x + y = 46.
you are given that 2/5 * the first part is equal to 3/4 of the other part.
the equation for that becomes 2/5 * x = 3/4 * y
to simplify further operations, multiply both sides of this equation by 20 to get:
2/5 * 20 * x = 3/4 * 20 * y
simplify to get:
8 * x = 15 * y.
you have two equations that need to be solved simultaneously.
they are:
x + y = 46
8x = 15y
solve for y in the first equation to get y = 46 - x.
replace y in the second equation with 46 - x to get:
8x = 15 * (46 - x)
distribute the multiplication on the right side of the equation to get:
8x = 15 * 46 - 15x
simplify to get 8x = 690 - 15x
add 15x to both sides of the equation to get:
8x + 15x = 690 - 15x + 15x becomes:
23x = 690
divide both sides of the equation by 23 to get:
x = 690 / 23 = 30.
since x + y = 46, this means that y must be equal to 16.
you have:
x = 30
y = 16
x + y = 30 + 16 = 46
8x = 15y becomes 8*30 = 15*16 which becomes 240 = 240.
this confirms the solution is good.
as further confirmation, you want to have 2/5 * x = 3/4 * y.
this becomes 2/5 * 30 = 3/4 * 16.
this becomes 60/5 = 48/4 which becomes 12 = 12.
your confirmation is final and your solution is good.
x = 30 and y = 16.
one part of the stick measures 30 meters and the other part of the stick measure 16 meters.
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