Use the drawing tool(s) to form the correct answers on the provided answer space.
Giles is making tacos for dinner and bought some beef and chicken. At the store, he bought twice as much beef as chicken. The chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Before sales tax, Giles spent a total of $12.95 on beef and chicken.
The system of equations below represent the pounds of chicken, [tex]$x$[/tex], and pounds of beef, [tex]$y$[/tex], that Giles purchased.
[tex]\begin{array}{c}
y=2 x \
1.85 x+3.7 y=12.95
\end{array}[/tex]
Part A: Use the ray tool to graph the system of equations on the coordinate plane.
Part B: Use the point tool to select the approximate pounds of beef Giles purchased.
Answer (2)
Giles purchased approximately 1.4 pounds of chicken and 2.8 pounds of beef. The relevant equations allow us to determine that he bought twice as much beef as chicken. Therefore, the answer for the pounds of beef is 2.8 pounds.
;
Substitute y = 2 x into the second equation: 1.85 x + 3.7 ( 2 x ) = 12.95 .
Simplify and solve for x : 9.25 x = 12.95 , so x = 1.4 .
Substitute x = 1.4 into y = 2 x to find y = 2.8 .
The approximate pounds of beef Giles purchased is 2.8 .
Explanation
Analyze the problem First, let's analyze the problem. We are given a system of two equations with two variables, x and y , representing the pounds of chicken and beef, respectively. The equations are:
y = 2 x 1.85 x + 3.7 y = 12.95
We need to find the values of x and y that satisfy both equations. This can be done by solving the system of equations.
Solve for x We can use the substitution method to solve this system. Since y = 2 x , we can substitute 2 x for y in the second equation:
1.85 x + 3.7 ( 2 x ) = 12.95
Now, we simplify and solve for x :
1.85 x + 7.4 x = 12.95 9.25 x = 12.95 x = 9.25 12.95 = 1.4
So, x = 1.4 pounds of chicken.
Solve for y Now that we have the value of x , we can find the value of y using the first equation:
y = 2 x = 2 ( 1.4 ) = 2.8
So, y = 2.8 pounds of beef.
Find the answer Therefore, Giles purchased 1.4 pounds of chicken and 2.8 pounds of beef. The question asks for the approximate pounds of beef Giles purchased, which is y .
Final Answer The approximate pounds of beef Giles purchased is 2.8 pounds.
Examples
Understanding systems of equations is useful in many real-world scenarios. For example, suppose you are planning a party and need to buy drinks and snacks. You have a budget and know the price of each item. You can set up a system of equations to determine the quantity of each item you can purchase within your budget. Similarly, in business, systems of equations can be used to optimize production, manage inventory, and analyze financial data. For instance, a company might use a system of equations to determine the optimal pricing strategy for its products, considering factors such as production costs, market demand, and competitor pricing. These models help in making informed decisions and maximizing profits.
