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There are blue, red, and green ribbons.

- The red ribbon is 3 inches more than twice the length of the blue ribbon.
- The green ribbon is one inch less than 3 times the length of the blue ribbon.

If the three ribbons measure 92 inches combined, what is the length of each ribbon?

Answer :

Sure! Let's find the lengths of the blue, red, and green ribbons step-by-step:

1. Define Variables:
- Let the length of the blue ribbon be [tex]\( x \)[/tex] inches.

2. Express Other Ribbons in terms of [tex]\( x \)[/tex]:
- The red ribbon is 3 inches more than twice the blue ribbon, so its length is [tex]\( 2x + 3 \)[/tex].
- The green ribbon is one inch less than three times the blue ribbon, so its length is [tex]\( 3x - 1 \)[/tex].

3. Write the Equation for Total Length:
- The total length of all three ribbons is 92 inches. Therefore, we can write the equation:
[tex]\[
x + (2x + 3) + (3x - 1) = 92
\][/tex]

4. Simplify the Equation:
- Combine like terms:
[tex]\[
x + 2x + 3x + 3 - 1 = 92
\][/tex]
[tex]\[
6x + 2 = 92
\][/tex]

5. Solve for [tex]\( x \)[/tex]:
- Subtract 2 from both sides:
[tex]\[
6x = 90
\][/tex]
- Divide both sides by 6:
[tex]\[
x = 15
\][/tex]

6. Find the Lengths of Each Ribbon:
- Blue Ribbon: [tex]\( x = 15 \)[/tex] inches.
- Red Ribbon: [tex]\( 2x + 3 = 2(15) + 3 = 30 + 3 = 33 \)[/tex] inches.
- Green Ribbon: [tex]\( 3x - 1 = 3(15) - 1 = 45 - 1 = 44 \)[/tex] inches.

Therefore, the blue ribbon is 15 inches, the red ribbon is 33 inches, and the green ribbon is 44 inches.

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