Amotorist paid $26.50 for 10 gallons of gas and 2 quarts of oil. another motorist paid $23.58 for 8 gallons of gas and 3 quarts of oil. find the cost of 1 gallon of gas and 1 quart of oil.

the cost of 1 gallon of gas is $2.31

the cost of 1 quart of oil is $1.7

Step-by-step explanation:

Let x represent the cost of 1 gallon of gas.

Let y represent the cost of 1 quart of oil.

A motorist paid $26.50 for 10 gallons of gas and 2 quarts of oil. It means that

10x + 2y = 26.5 - - - - - - - -1

Another motorist paid $23.58 for 8 gallons of gas and 3 quarts of oil. This means that

8x + 3y = 23.58 - - - - - - -- - - - 2

Multiplying equation 1 by 3 and equation 2 by 2, it becomes

30x + 6y = 79.5

16x + 6y = 47.16

Subtracting, it becomes

14x = 32.34

x = 32.34/14 = 2.31

Substituting x = 2.31 into equation 1, it becomes

10 ×2.31 + 2y = 26.5

23.1 + 2y = 26.5

2y = 26.5 - 23.1 = 3.4

y = 3.4/2 = 1.7