SOLUTION: I have a story problem that I need to translate into an equation and solve (with a Let statement). It's easy for me to solve equations, but translating a story problem is just dif

Algebra ->  Equations -> SOLUTION: I have a story problem that I need to translate into an equation and solve (with a Let statement). It's easy for me to solve equations, but translating a story problem is just dif      Log On


   

Question 185511: I have a story problem that I need to translate into an equation and solve (with a Let statement). It's easy for me to solve equations, but translating a story problem is just difficult and confuses me.
The problem:
A board 190cm long is cut into three pieces. The second piece is three times the length of the first piece and the third piece is 10cm longer than twice the first piece. How long is each of the three pieces?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = length of first piece, y = length of second piece, and z = length of third piece



Since "The second piece is three times the length of the first piece", this tells us that y=3x and because "the third piece is 10cm longer than twice the first piece", this means that z=2x%2B10


Now the the sum of the three pieces should be equal to the total original length 190. In other words, x%2By%2Bz=190


x%2By%2Bz=190 Start with the given equation.


x%2B3x%2B2x%2B10=190 Plug in y=3x and z=2x%2B10


6x%2B10=190 Combine like terms on the left side.


6x=190-10 Subtract 10 from both sides.


6x=180 Combine like terms on the right side.


x=%28180%29%2F%286%29 Divide both sides by 6 to isolate x.


x=30 Reduce.


So the first piece is 30 cm

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y=3x Go back to the first equation


y=3%2830%29 Plug in x=30


y=90 Multiply


So the second piece is 90 cm

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z=2x%2B10 Go back to the second equation


z=2%2830%29%2B10 Plug in x=30


z=60%2B10 Multiply


z=70 Add


So the third piece is 70 cm


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Answer:


So the lengths of the three pieces are

1st: 30 cm
2nd: 90 cm
3rd: 70 cm