a total of 17 cars and trucks get gasoline at the gas station. Each car gets 8 gallons of gasoline. Each truck gets 19 gallons of gasoline. The station sells 169 gallons of gasoline. How many cars were at the gas station? How many trucks were at the gas station?

Answer:There were 14 cars and 3 trucks at the gas stationStep-by-step explanation:This problem can be modeled by a system of equations.I am going to say that x is the number of cars at the gas station and y is the number of trucks at the gas station.The problem states that there were a total of 17 cars and trucks get gasoline at the gas station. It means that x + y = 17.The problem also states that each car gets 8 gallons of gasoline and each truck gets 19 gallons of gasoline, and that the station sells 169 gallons of gasoline. So 8x + 19y = 169.So, we have a system with these following equations:1) x + y = 172) 8x + 19y = 169I am going to write x as a function of y in 1) and replace it in 2)x = 17 - y8(17 - y) + 19y = 16911y = 169 - 13611y = 33y = 3So, there were 3 trucks at the gas station.From 1)x = 17 - yx = 17 - 3x = 14There were 14 cars at the gas station.