Question

Find two numbers, if their sum is 49 and their difference is 1/2 .

Answer 1

Answer:

x+y=49------(1)

x-y=1/2--------(2)

add eqn. (1)and(2)

x+y+x-y=49+1/2

2x=99/2

x=99/4

Step-by-step explanation:

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Answer 2

Answer:

The two numbers are $\frac{99}{4}$ and $\frac{97}{4}$.

Step-by-step explanation:

Consider that the two unknown numbers are denoted by: x and y.

Using the provided information, two equations relating to x and y can be formed as follows:

$x+y=49\ \ ...(i)\\\\x-y=\frac{1}{2}\ \ \ ...(ii)$

The process of determining the values of x and y involves solving equations (i) and (ii) simultaneously.

Simultaneously solve equations (i) and (ii) for x:

$x+y=49\\\\x-y=\frac{1}{2}\\\_\_\_\_\_\_\_\_\_\_\_\_\_\ \ \ \ \ \ (Add\ both\ equations)\\\\2x=\frac{98+1}{2}\\\\x=\frac{99}{2}\times \frac{1}{2}\\\\x=\frac{99}{4}$

The value of x is $\frac{99}{4}$.

Using the value of x in equation (i), solve for y:

$x+y=49\\\\\frac{99}{4}+y=49\\\\y=49-\frac{99}{4}\\\\y=\frac{196-99}{4}\\\\y=\frac{97}{4}$

The value of y is $\frac{97}{4}$.