To understand whether the given information is enough to determine the cost of 1 gallon of gasoline and 1 quart of oil, we will write an equation for each case. Let x be the cost of 1 gallon of gasoline and y be the cost of 1 quart of oil
Verbal Expression
My Receipt
My Friend's Receipt
Cost of gasoline ($)
10 x
5 x
Cost of oil ($)
2 y
y
Total cost ($)
10 x+2 y=45.50
5 x+ y=22.75
With this information we can write a system of two equations.
10x+2y=45.50 & (I) 5x+y=22.75 & (II)
Notice that multiplying Equation (II) by 2 results in Equation (I). This means that the equations are the same, so the given information is not enough to determine the costs of gasoline and the oil.
b
On the receipt we can see that 8 gallons of gasoline and 2 quarts of oil cost $38.40 in total. We can write an equation for the receipt by proceeding in the same way as we did in Part A.
8x+2y=38.40
If we combine it with one of the previous equations into a system, we can see that there is no proportion between coefficients of equations.
10x+2y=45.50 & (I) 8x+2y=38.40 & (II)
Therefore, we can conclude that these equations are different and we can determine the cost of 1 gallon of gasoline and 1 quart of oil.
c
In order to determine the cost of 1 gallon of gasoline and 1 quart of oil, we will use the system in Part B.
10x+2y=45.50 & (I) 8x+2y=38.40 & (II)
Notice that the y-variable has the same coefficient. Therefore, we can use Elimination Method to solve the system. Let's start!
