A number x lies between the cubes of 6 and 8 in such a way that if you add or subtract the number y from it you will get the cube of 8 or 6 respectively. Find the numbers x and y. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

The number x lies between the cube of 6 and 8 i.e between 216 and 512

Also Given

x + y = cube of 8 = 512.............(1)
x - y = cube of 6 =216................(2)

Adding Equation (1) and (2), we get

$\Rightarrow 2 x = 512 + 216$
$\Rightarrow x = 364$

Substituting the value of x in eq.(1)

$\Rightarrow 364 + y = 512$
$\Rightarrow y = 148$

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