Inspired by Tanishq Varshney

Algebra Level 4

⌊ 2 x ⌋ + ⌊ y ⌋ = 5 \large \displaystyle \lfloor 2x \rfloor + \lfloor y \rfloor = 5

Find the area bounded by the set of points in the first quadrant that satisfy the equation above.

Inspiration .


The answer is 3.

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Vishwak Srinivasan by Vishwak Srinivasan , 24, India

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1 solution

Plot the graph of the given functions taking separate intervals in x x , like [ 0 , 1 2 ] , [ 1 2 , 1 ] [0,\frac{1}{2}] , [\frac{1}{2},1] and so on.

You will then get suitable values of ⌊ y ⌋ \lfloor y \rfloor which then gives a range of values for y y .

The graph will be in the form of blocks, 6 in number, each having area 1 2 \frac{1}{2} sq.units.

6 × 1 2 = 3 ⇒ 6 \times \frac{1}{2} = \boxed{3} \Rightarrow the required ans.

2 Helpful 0 Interesting 1 Brilliant 0 Confused

When I solved, I found that the points in between -2x+5 and -2x+6 (on the first quad) satisfy the equation and the intger area between them appears to be 3.

First Last - 5 years, 6 months ago

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