Test Index

Ratio and Proportion

Question : 45 of 112

Marks: +1, -0

Solution:

Concept:

Form equations from given relationships and solve for the shortest piece's length.

Explanation:

Let the longest piece be

L

, the middle piece be

M

, and the shortest piece be

S

Given:

L = 3M

and

S = L - 23

Total length:

L + M + S = 40

Substitute

L = 3M

and

S = 3M - 23

into the total equation:

3M + M + (3M - 23) = 40

7M - 23 = 40

7M = 63

M = 9

cm.

Then

L = 3 \times 9 = 27

cm, and

S = 27 - 23 = 4

cm.

Answer:

The shortest piece is 4 cm.

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