Question

The difference of two numbers is 7. Two times the smaller is 4 more than the larger. Find the two numbers.[1/1]2 (0/1)B0/1)The two numbers areand

Answer 1

`18,11`

1) In this question, we are going to tackle this thinking of two variables.

2) As we were told that the difference is 7, and the second number has been described let's write them down:

`\begin{gathered} x-y=7 \\ 2y=4+x \end{gathered}`

The smaller one: "y", the greater one: x

3) So now, let's solve this System of Linear equations by the Method of Substitution plugging into the 1st equation the second one. But before that, we need to rewrite:

`\begin{gathered} 2y=4+x \\ (2y)/(2)=(4+x)/(2) \\ y=2+(x)/(2) \end{gathered}`

3.2) Now we can plug this into the 1st equation:

`\begin{gathered} x-(2+(x)/(2))=7 \\ x-2-(x)/(2)=7 \\ (x)/(2)-2=7 \\ (x)/(2)=7+2 \\ (2*)(x)/(2)=9(*2) \\ x=18 \end{gathered}`

Now, let's plug into one of those original equations the quantity of x:

`\begin{gathered} x-y=7 \\ 18-y=7 \\ -y=-18+7 \\ -y=-11 \\ y=11 \end{gathered}`

Thus, the two numbers are 18 and 11.