a 132 inch lenght of ribbon is to be cut into 3 pieces the longest piece is to be 39 inches longer than the shortest piece and the third piece is to be half the length of the longest piece find the length of each piece of ribbon
let the shortest be x inches
let the longest piece be x+39
let the other piece be (1/2)(x+39)
x + x+39 + (1/2)(x+39) = 132
don't like fractions, so multiply everybody be 2
2x + 2x + 78 + x+39 = 264
5x = 147
x = 29.4 inches
shortest is 29.4 inches
longest is 68.4 inches
other is 34.2 inches
check:
29.4+68.4+34.2 = 132
To solve this problem, we can set up equations based on the given information and then solve them.
Let's assume the length of the shortest piece of ribbon is "x" inches.
According to the problem, the longest piece is 39 inches longer than the shortest piece. So we can write the equation:
Longest piece = x + 39
The third piece is half the length of the longest piece. So we can write the equation:
Third piece = (1/2) * (x + 39)
We know that the sum of the lengths of the three pieces equals the total length of the ribbon, which is 132 inches. So we can write the equation:
x + (x+39) + (1/2) * (x+39) = 132
Now we can solve this equation step by step:
Multiply (1/2) * (x+39) to get (x+39)/2:
x + (x+39) + (x+39)/2 = 132
Multiply every term by 2 to eliminate the fraction:
2x + 2(x+39) + (x+39) = 264
Simplify:
2x + 2x + 78 + x + 39 = 264
Combine the x terms:
5x + 117 = 264
Subtract 117 from both sides to isolate the variable:
5x = 147
Divide both sides by 5 to solve for x:
x = 29.4
So the length of the shortest piece is approximately 29.4 inches.
Now we can find the lengths of the other pieces:
Longest piece = x + 39 = 29.4 + 39 = 68.4 inches
Third piece = (1/2) * (x + 39) = (1/2) * (29.4 + 39) = 34.7 inches
Therefore, the lengths of the three pieces of ribbon are approximately:
Shortest piece: 29.4 inches
Longest piece: 68.4 inches
Third piece: 34.7 inches