Question

For each word problem, identify the variables, write equations and solve.

Answer 1

One number is 56 and the other 36

Explanation:

Starting from the statement we have the following system of equations: let x be a number and y and the other.

`\begin{gathered} x+y=92\text{ (1)} \\ x-y=20\text{ (2)} \end{gathered}`

We solve the system of equations by substitution

`\begin{gathered} x+y=92\rightarrow x=92-y\text{ (3)} \\ \text{replacing (3) in (2)} \\ 92-y-y=20 \\ -2y=20-92 \\ y=(-72)/(-2) \\ y=36 \end{gathered}`

now, for x, replacing y in (3)

`\begin{gathered} x=92-36 \\ x=56 \end{gathered}`