Question

Set up an equation to solve the given word problem

Answer 1

Let a and b be two numbers. The first equation described in the sentence is

`a=22+b`

And the second equation is

`ab=-121`

Notice that the first equation implies that b>a, so we can rename b as x, obtaining the next two equations

`\begin{gathered} a=22+x \\ ax=-121 \end{gathered}`

Then,

`\begin{gathered} \Rightarrow ax=(22+x)x \\ \Rightarrow x(22+x)=-121 \\ \Rightarrow x(x+22)=-121 \end{gathered}`

The answer is option c.

Finally, solve the equation above for x, as shown below

`\begin{gathered} x(x+22)=x^2+22x \\ \Rightarrow x^2+22x=-121 \\ \Rightarrow x^2+22x+121=0 \\ \Rightarrow(x+11)^2=0 \\ \Rightarrow x+11=0 \\ \Rightarrow x=-11 \end{gathered}`

The answer is x= -11

And number a is x+22=-11+22, a=11