Question

Person A weighs 350 pounds and starts losing 3 pounds a month while on a new workout plan. Person B weighs 300 and starts losing 1 pound a month on the same workout plan. Write an equation/inequality to show when person A will weigh less than Person B.

Answer 1

Person A.

Weighs 350 pounds and starts losing 3 pounds a month while on a new workout plan.

We can express this situation like the following

`A=350-3m`

Where m is months.

Person B.

Weighs 300 and starts losing 1 pound a month on the same workout plan.

We can express this situation like the following

`B=300-m`

Where m is months.

Now, the problem is asking for the case when Person A will weigh less than Person B, this can be expressed like

Then, we solve for m

`\begin{gathered} -3m+m<300-350 \\ -2m<-50 \end{gathered}`

At last, we divide the inequality by -2, this will change the sign

`\begin{gathered} (-2m)/(-2)>(-50)/(-2) \\ m>25 \end{gathered}`

Therefore, after 25 months, Person A will weigh less than Person B.