Chapter MPS, Problem 2.9MPS

(a)

To determine

To Find: The inequality that represents the given situation

Answer to Problem 2.9MPS

  $g\left(\$4.03\right)+q\left(\$2.99\right)\le \$65$

Explanation of Solution

Given:

  $\begin{array}{l}\text{→}\text{Gas cost per gallon}=\$4.03\\ \text{→}\text{Oil cost per quart}=\$2.99\\ \text{→}\text{Total money jerome can spend}=\$65\\ \text{→}\text{Number of gallons of gas}=g\\ \text{→}\text{Number of quarts of oil}=q\end{array}$

Formula Used:

  $\text{Gas cost}+\text{oil cost}\le \text{Total money to spent}$

Calculation:

  $\begin{array}{l}\text{→}\text{Gas cost per gallon}=\$4.03\\ \text{→}\text{Oil cost per quart}=\$2.99\\ \text{→}\text{Total money jerome can spend}=\$65\\ \text{→}\text{Number of gallons of gas}=g\\ \text{→}\text{Number of quarts of oil}=q\\ \text{The inequality that represents the situation is :}\\ \text{→}\text{Gas cost}+\text{oil cost}\le \text{Total money}\\ \text{⇒}g\left(\$4.03\right)+q\left(\$2.99\right)\le \$65\end{array}$

Conclusion:

Thus the inequality that represents the given situation is $g\left(\$4.03\right)+q\left(\$2.99\right)\le \$65$

(b)

To determine

To Find: The graph of the inequality

Answer to Problem 2.9MPS

Explanation of Solution

Given:

  $\begin{array}{l}\text{→}\text{Gas cost per gallon}=\$4.03\\ \text{→}\text{Oil cost per quart}=\$2.99\\ \text{→}\text{Total money jerome can spend}=\$65\\ \text{→}\text{Number of gallons of gas}=g\\ \text{→}\text{Number of quarts of oil}=q\end{array}$

Formula Used:

  $\text{Gas cost}+\text{oil cost}\le \text{Total money to spent}$

Calculation:

  

Conclusion:

Thus the graph of the given inequality is represented in calculation section.

(c)

To determine

To Find: The solution of the given condition

Answer to Problem 2.9MPS

  $\text{Total money spent by Jerome}=\$72.28$

Explanation of Solution

Given:

  $\begin{array}{l}\text{→}\text{Gas cost per gallon}=\$4.03\\ \text{→}\text{Oil cost per quart}=\$2.99\\ \text{→}\text{Total money jerome can spend}=\$65\\ \text{→}\text{Number of gallons of gas}=12\\ \text{→}\text{Number of quarts of oil}=8\end{array}$

Formula Used:

  $\text{Gas cost}+\text{oil cost}=\text{Total money to spent}$

Calculation:

  $\begin{array}{l}\text{→}\text{Gas cost per gallon}=\$4.03\\ \text{→}\text{Oil cost per quart}=\$2.99\\ \text{→}\text{Total money jerome can spend}=\$65\\ \text{→}\text{Number of gallons of gas}=12\\ \text{→}\text{Number of quarts of oil}=8\\ \text{Total money spent by Jerome}=\text{Money spent on gas}+\text{money spent on oil}\\ \text{⇒}\text{Total money spent by Jerome}=\left(12\right)\left(\$4.03\right)+\left(8\right)\left(\$2.99\right)\\ \text{⇒}\text{Total money spent by Jerome}=\$48.36+\$23.92\\ \text{⇒}\text{Total money spent by Jerome}=\$72.28\end{array}$

Conclusion:

Thus the total money spent by Jerome is $\$72.28$