Chapter 8.3, Problem 9E

To determine

To write:

An equation describing the possible amounts of ground beef and chicken that you can buy. Use intercepts to graph the equation.

Answer to Problem 9E

Our required equation would be $3x+5y=30$ .

x -intercept: $(10,0)$

y -intercept: $(0,6)$

Explanation of Solution

Given:

You are in charge of buying food for a barbecue. You have budgeted $30 for ground beef and chicken. Ground beef costs $3 per pound, and chicken costs $5 per pound.

Calculation:

Let x represent the pounds of ground beef and y represent the pounds of chicken.

We have been given that ground beef costs $3 per pound, so cost of x pounds of ground beef would be $3x$ .

We have been given that chicken costs $5 per pound, so cost of y pounds of chicken would be $5y$ .

Since the budget for buying food is $30, so cost of x pounds of ground beef and y pounds of chicken would be equal to $30. We can represent this information in an equation as:

  $3x+5y=30$

Therefore, our required equation would be $3x+5y=30$ .

To find x -intercept, we will substitute $y=0$ in our given equation and solve for xas shown below:

  $\begin{array}{l}3x+5y=30\left(\text{Given equation}\right)\\ 3x+5(0)=30\left(\text{Substituting }y=0\right)\\ 3x=30\\ \frac{3x}{3}=\frac{30}{3}\\ x=10\end{array}$

Therefore, the x -intercept of our given equation is $(10,0)$ .

To find y- intercept, we will substitute $x=0$ in our given equation and solve for yas shown below:

  $\begin{array}{l}3x+5y=30\left(\text{Given equation}\right)\\ 3(0)+5y=30\left(\text{Substituting }x=0\right)\\ 5y=30\\ \frac{5y}{5}=\frac{30}{5}\left(\text{Dividing both sides by 5}\right)\\ y=6\end{array}$

Therefore, the y -intercept of our given equation is $(0,6)$ .

Upon graphing our given equation, we will get our required graph as shown below: