Chapter 5, Problem 12CT

a.

To determine

To check: Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil.Explain.

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 $a$ be the cost of 1 gallon of gasoline and $b$ be the cost of 1 quart of oil.

So using above given information we can write 2 equations

  $10a+2b=\mathrm{45.50...}(i)$

  $5a+b=\mathrm{22.75...}(ii)$

Now dividing equation (i) by 2, we get

  $5a+b=\mathrm{22.75...}(iii)$

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 determine

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.

  

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 $a$ be the cost of 1 gallon of gasoline and $b$ be the cost of 1 quart of oil.

So using above given information we can write 2 equations

  $8a+2b=\mathrm{38.45...}(iv)$

  $10a+2b=\mathrm{45.50...}(v)$

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 determine

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.

  

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

  $8a+2b=\mathrm{38.45...}(iv)$

  $10a+2b=\mathrm{45.50...}(v)$

Calculation: Subtracting equation (iv) from (v), we get

  $(10-8)a=45.50-38.45$

  $2a=7.1\to a=3.55$

Now putting value of $a$ in equation (v), we get

  $8*3.55+2b=38.40$

  $2b=10\Rightarrow b=5$

Conclusion: The cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.