A rational number is such that when we multiply it by 52 and add 23 to the product we get -712- What is the number-

Let the rational number be x .When we multiply it by 52 and add 23 to the product we get 712 .i.e., x ×52 + 23 = 712 5x2 = 71 ...

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Standard VIII

Mathematics

Applications (Word Problem)

A rational nu...

Question

A rational number is such that when we multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product we get $\frac{- 7}{12}$ . What is the number?

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Solution

Let the rational number be $x$ .
When we multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product we get $\frac{- 7}{12}$ .
i.e., $x \times \frac{5}{2} + \frac{2}{3} = \frac{- 7}{12}$
$\frac{5 x}{2} = \frac{- 7}{12} - \frac{2}{3}$
$= \frac{- 7 - 8}{12}$
$= \frac{- 15}{12}$
$x = \frac{- 15}{12} \times \frac{2}{5}$
$= \frac{- 1}{2}$ .
Hence the required number is $\frac{- 1}{2}$ .
Verification:
$L H S = \frac{- 1}{2} \times \frac{5}{4} + \frac{2}{3} = \frac{- 5}{4} + \frac{2}{3}$
$= \frac{- 15 + 8}{12} = \frac{- 7}{12} = R H S$ .

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A rational number is such that when we multiply it by 52 and add 23 to the product we get −712. What is the number?

Let the rational number be x.When we multiply it by 52 and add 23 to the product we get −712.i.e., x×52+23=−7125x2=−712−23=−7−812=−1512x=−1512×25=−12.Hence the required number is −12.Verification:LHS=−12×54+23=−54+23=−15+812=−712=RHS.

A rational number is such that when we multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product we get $\frac{- 7}{12}$ . What is the number?