p(t) = 1000 subsitute variables into equation

\(\displaystyle{p}{\left({t}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{c}\)

\(\displaystyle{\left({1000}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{\left({900}\right)}\)

\(\displaystyle{0}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{1900}\)

\(\displaystyle{200}{t}^{{2}}-{2500}{t}+{1900}={0}\)

a = 200, b = -2500 c = 1900 quadratic equation

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{2500}^{{2}}-{4}{\left({200}\right)}{\left({1900}\right)}}}}}{{2}}{\left({200}\right)}\)

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{4730000}}}}}{{400}}\)

\(\displaystyle{t}=\frac{{25}}{{4}}+\frac{\sqrt{{{473}}}}{{4}}\)

\(\displaystyle{t}=\frac{{25}}{{4}}-\frac{\sqrt{{{473}}}}{{4}}\)

\(\displaystyle{t}={6.25}+{5.43714079273}=\${11.69}\) or

\(\displaystyle{t}={6.25}-{5.43714079273}=\${0.81}\)

saltillo plaza: c = 1500

p(t) = 1000 subsitute variables into equation

\(\displaystyle{p}{\left({t}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{c}\)

\(\displaystyle{\left({1000}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{\left({1500}\right)}\)

\(\displaystyle{0}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{2500}\)

\(\displaystyle{200}{t}^{{2}}-{2500}{t}+{2500}={0}\)

a = 200, b = -2500 c = 2500 quadratic equation

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{2500}^{{2}}-{4}{\left({200}\right)}{\left({2500}\right)}}}}}{{2}}{\left({200}\right)}\)

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{4250000}}}}}{{400}}\)

\(\displaystyle{t}=\frac{{25}}{{4}}+{\left(\frac{{5}}{{4}}\right)}\sqrt{{{17}}}=\${11.40}\) or

\(\displaystyle{t}=\frac{{25}}{{4}}-{\left(\frac{{5}}{{4}}\right)}\sqrt{{{17}}}=\${1.09}\)

riverside walk: c = 2500

p(t) = 1000 subsitute variables into equation

\(\displaystyle{p}{\left({t}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{c}\)

\(\displaystyle{\left({1000}\right)}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{\left({2500}\right)}\)

\(\displaystyle{0}=-{200}{\left({t}^{{2}}\right)}+{2500}{t}-{3500}\)

\(\displaystyle{200}{t}^{{2}}-{2500}{t}+{3500}={0}\)

a = 200, b = -2500 c = 3500 quadratic equation

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{2500}^{{2}}-{4}{\left({200}\right)}{\left({3500}\right)}}}}}{{2}}{\left({200}\right)}\)

\(\displaystyle{t}=\frac{{{2500}\pm\sqrt{{{3450000}}}}}{{400}}\)

t = $10.89 or

t = $1.61