If a weekend special is for 2 nights and 3 meals for $195, and another cost is 3 nights and 5 meals for $300, what is the meal price and how much does each night cost?

x = night

y = meal

2x + 3y = 195--------> -6x - 9y = -585 {multiplied top equation by -3}

3x + 5y = 300--------> 6x + 10y = 600 {multiplied bottom equation by 2}

y = 15 {added the two new equations together}

2x + 3y = 195 {top equation}

2x + 3(15) = 195 {substituted 15, in for y, into top equation}

2x + 45 = 195 {multiplied 3 by 15}

2x = 150 {subtracted 45 from both sides}

x = 75 {divided both sides by 2}

meal = $15

night = $75

© Algebra House

y = meal

2x + 3y = 195--------> -6x - 9y = -585 {multiplied top equation by -3}

3x + 5y = 300--------> 6x + 10y = 600 {multiplied bottom equation by 2}

y = 15 {added the two new equations together}

2x + 3y = 195 {top equation}

2x + 3(15) = 195 {substituted 15, in for y, into top equation}

2x + 45 = 195 {multiplied 3 by 15}

2x = 150 {subtracted 45 from both sides}

x = 75 {divided both sides by 2}

meal = $15

night = $75

© Algebra House