# 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?

Sep 5, 2017

See explanation

#### Explanation:

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

$\textcolor{b l u e}{C o n \mathrm{di} t i o n \left(1\right)}$

Minimum of 25 $y \to y \ge 25$

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$\textcolor{b l u e}{C o n \mathrm{di} t i o n \left(2\right)}$

At least 40 $r \mathmr{and} y$

$r + y \ge 40$

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$\textcolor{b l u e}{C o n \mathrm{di} t i o n \left(3\right)}$

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

So $r \ge 15$

$\textcolor{b l u e}{\text{The shaded area is the feasible region}}$