SOLUTION: How do you Use an algebraic approach to solve the problem. A board 45 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the othe

Question 628054: How do you Use an algebraic approach to solve the problem.
A board 45 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.
so far what i have is 2/3x=45 is this right? if so how do you solve?
Found 3 solutions by reviewermath, richwmiller, solver91311:
Answer by reviewermath(1029)   (Show Source): You can put this solution on YOUR website!
Let x = length of one piece
so 45 - x = length of the other piece
, multiply both sides by 3

and
Answer: The length of the shorter piece is 18 feet.

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
close but not quite.
you have two pieces that add up to 45
x+y=45
x is the longer one.
the other y =2x/3
so now we have
two equations with two unknowns
x+y=45
y=2x/3
substitute
x+2x/3=45
3x/3+2x/3=45
5x/3=45
divide by 5
x/3=9
x=27
2*27/3=18=y
check
27+2*27/3=45
27+18=45
45=45
ok
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let's see if your approach makes sense. You said . If a part of the quantity is equal to 45, then must be bigger than 45. If I asked you for two-thirds of the money in your wallet and you handed me $45, you must have started with more than the 45 bucks, right? That means, according to your theory, that one of the pieces of board is longer than the piece it was cut from. Absurd in the extreme.

Read the problem carefully. I'm going to assign to represent the measure of the longer piece, just because it is easier to explain the problem that way. Generally you will want to assign your variable to represent the quantity asked for by the problem, but that is just a little inconvenient this time.

Let represent the measure of the longer piece. Then we are given that is the measure of the shorter piece. Together (except for a negligible saw kerf) the two boards should add up to the original 45 feet.

Solve for and then calculate

Step 1: Multiply both sides by 3:

Step 2: Collect like terms:

Step 3: Multiply by the reciprocal of the coefficient on the variable:

Which is the measure of the larger piece. You can either calculate or to find the measure of the shorter piece.

John

My calculator said it, I believe it, that settles it

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