Question

3. The sum of two numbers is 105 and the difference of the two numbers is 21. What are the two numbers? a) (65, 15) b) (70,49) c) (63,42) d) (65, 41) b

Answer 1

The first statement can be written mathematically as

`x+y=105`

and the second statement can be written as

`x-y=21`

Hence, we have 2 equations in 2 unknows. We can solve this system by elimination:

If we add these equations, we have

`\begin{gathered} 2x+0=105+21 \\ \text{this gives } \\ 2x=84 \end{gathered}`

therfore,

`\begin{gathered} x=(84)/(2) \\ x=42 \end{gathered}`

Since we know x, we can substitute this value into the first equation, It yields

`42+y=105`

and now we can isolate y:

`\begin{gathered} y=105-42 \\ y=63 \end{gathered}`

Finally, the answer is (63,42)