a.
To check: Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil.Explain.
a.
Answer to Problem 12CT
The given information is not enough to determine the cost of 1 gallon of gasoline and 1 quart of oil.
Explanation of Solution
Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 5 gallons of gasoline and 1 quarts of oil is $22.75.
Calculation: Let
So using above given information we can write 2 equations
Now dividing equation (i) by 2, we get
Now we can see that equation (ii) and (iii) are same, it means we can say that we are not given 2 different equations ,we are given 1 equation with two variables. Therefore we cannot find the values of variables.
Conclusion: The given information is not enough to determine the costs.
b.
To calculate: You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.
b.
Answer to Problem 12CT
Yes, we can find the cost of 1 gallon and 1 qart.
Explanation of Solution
Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 8 gallons of gasoline and 2 quarts of oil is $38.45.
Calculation: Let
So using above given information we can write 2 equations
Here from equation (iv) and (v) we can say that we have 2 different equations with 2 variables, So we can find the value of both variables.
Conclusion: We can determine the costs.
c.
To calculate: You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. Determine the cost of 1 gallon of gasoline and 1 quart of oil.
c.
Answer to Problem 12CT
Cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.
Explanation of Solution
Given information: From the above part we have
Calculation: Subtracting equation (iv) from (v), we get
Now putting value of
Conclusion: The cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.
Chapter 5 Solutions
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