Question

1) alice decides to take a trip from the east coast of the united states to the west coast. while planning, she chooses to drive, fly, and ride a train. her first leg of the trip is traveling by car, from sacramento, california to denver, colorado. along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. after driving for many hours, alice finally makes it to denver, colorado spending $874.80 in gas. a) let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. create an equation that models the situation.

Answer 1

The equation will be: 4.65r + 4.95p = 874.80

The total cost of gas will be sum of the individual costs of both the types of gas. Firstly, calculating cost of regular and premium gas followed by forming the equation.

The total cost of regular gas = Amount of regular gas × Cost of regular gas per gallon

The total cost of regular gas = 4.65 × r

The total cost of premium gas = Amount of premium gas × Cost of premium gas per gallon

The total cost of regular gas = 4.95 × p

We are given overall spending = 874.80

Forming the equation -

Total cost of regular gas + total cost of premium gas = overall spending on gas

4.65r + 4.95p = 874.80

Hence, the equation that models the situation is 4.65r + 4.95p = 874.80.

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