Question

Allie has two cars- a truck and a sedan. Last week, she used 3 gallons of gas in the truck and 5 gallons of gas in the sedan and drove 181 miles. This week she used 7 gallons of gas in the truck and 6 gallons of gas in the sedan and drove 275 miles. Find the average gas mileage for each vehicle.

Answer 1

sedan = 26 miles/gallon

truck = 17 miles/gallon

Explanation:

try to write the text in mathematical format as a system of equations

t=truck s=sedan

`\left \{ {{3t+5s=181} \atop {7t+6s=275}} \right.`

first equation can be written as

t= (181-5s)/3

we can use it in the second equation and rewrite it as

7[(181-5s)/3]+6s = 275

7(181/3 -5/3s) + 6s = 275

1267/3 - 35/3s + 6s = 275

-35/3s + 18/3s = 275-1267/3

-35/3s + 18/3s = 825/3 - 1267/3

-35s + 18s = 825 -1267

-17s = -442 s = 442/17 = 26 sedan has an average of 26 miles/gallon

we use this value of s in the first equation

3t + 5*26=181 3t=181-130 t= 51/3 = 17 truck has an average of 17 miles/gallon