Question

You want to decorate a party hall with a total of at least 40 red and yellow balloons, with a minimum of 25 yellow balloons. How do you write and graph a system of inequalities to model the situation?

Answer 1

See explanation

Explanation:

Set red balloon count as `r`
Set yellow balloon count as `y`

`color(blue)(Condition(1))`

Minimum of 25 `y -> y>=25`

.............................................................................
`color(blue)(Condition(2))`

At least 40 `r and y`

`r+y>=40`

..........................................................................
`color(blue)(Condition(3))`

Thus the minimum `r->40-25->15color(red)(larr" Corrected "40=25" to "40-25`

So `r>=15`

`color(blue)("The shaded area is the feasible region")`