Find the value!

Algebra Level 2

Let $x$ and $y$ be real numbers satisfying $5x=5y$ .

If we also assume that $x$ and $y$ belongs to the set of natural numbers $\mathbb N$ , then the least possible value of $x+y$ is denoted by $A$ .

But if we assume that $x$ and $y$ belongs to the set of whole numbers, then the least possible value of $x+y$ is denoted by $B$ .

Find $A+B$ .

The answer is 2.

2 solutions

Nashita Rahman
May 29, 2016

5 x = 5 y or , x = y

case 1: x&y are natural numbers. therefore, least possible value of x=y=1

x+y=2=A

case 2: x&y are whole numbers. therefore ,least possible value of x=y=0

x+y=0=B

Hence, A+B=2+0=2 (answer)

What do you mean by "whole numbers"? This can be interpreted as integers... also, 0 belongs to the set of natural numbers, so the answer is not correct.

Mateo Matijasevick - 5 years ago

Some authors begin the natural numbers with 0, corresponding to the non-negative integers $0, 1, 2, 3, …,$ whereas others start with $1$ corresponding to the positive integers $1, 2, 3,..$ . Those who treat Natural numbers set as, $\mathbb N = \{ 1, 2, 3,...\}$ they usually take whole numbers as set of natural numbers including zero that is, $\mathbb W = \{0, 1, 2,3,...\} = \mathbb Z^{+}$

akash patalwanshi - 5 years ago

The basic difference between whole numbers and natural numbers is that whole numbers begin from zero where as natural numbers begin from 1. Natural numbers are usually considered to be positive non-zero integers.

Nashita Rahman - 5 years ago

Prince Loomba
Dec 31, 2016

$5x=5y$ implies $x=y$

Now for $x+y=2x$ to be least, the value of $x$ should be least.

In first case, least $\color{#D61F06}x=1$ and in second case, least $\color{#3D99F6}x=0$ .

So $\color{#D61F06}A=2x=2×1=2$ and $\color{#3D99F6}B=2x=2×0=0$

So $\color{#20A900}A+B=2+0=\boxed {2}$

Find the value!

The answer is 2.

2 solutions

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