Question

A metal pipe $ 3 $ meter long was found to weigh $ 7.6 $ kg. what would be the weight of the same kind of $ 7.8 $ m long pipe?

Answer 1

Hint: Here we will understand the given data and frame the equation in the form of mathematical expression using the cross-multiplication and then simplifying the expression for the required resultant value.

Complete step-by-step answer:
 $ 3 $ meter pipe $ = 7.6 $ kg
 $ 7.8 $ meter pipe $ = ? $
Cross multiply the above expression, left hand side of one equation is multiplied with the opposite side of the other equation –
 $ = \dfrac{{7.6 \times 7.8}}{3} $
Simplify the above expression –
 $ = \dfrac{{76 \times 78}}{{10 \times 10 \times 3}} $
Find the factors of the above expression on the numerator –
 $ = \dfrac{{76 \times 26 \times 3}}{{10 \times 10 \times 3}} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
 $ = \dfrac{{76 \times 26}}{{10 \times 10}} $
Find the product of the terms on the numerator –
 $ = \dfrac{{1976}}{{100}} $
Convert the above expression in the form of the decimal.
 $ = 19.76 $ kg.
Hence, the weight of the same kind of $ 7.8 $ m long pipe is $ 19.76 $ kg.

Note: Be careful while cross multiplication and the sides while placing the term, the term on the denominator is multiplied with the numerator of the opposite side and the numerator of one side is multiplied with the opposite side of the denominator. Be careful while placing the decimal point based on the number of zeros in the denominator.