Question

shared task set
mayur is in charge of creating themed popcorn containers for a county fair. he plans on creating cylindrical and cone - shaped containers. each cylindrical container, x, has a volume of 52 in³, and each cone - shaped container, y, has a volume of 26 in³. both containers have a height of 5.5 in
the system of equations shown can be used to find the number of cylindrical and cone - shaped containers at each snack booth in the fair.
52x + 26y = 7150
x + y = 175
determine how many cylindrical containers, x, and cone - shaped containers, y, will be at each snack booth in the fair.

Explanation:

Step1: Solve the system of equations. We have the system:

$$\begin{cases} 52x + 26y = 7150 \\ x + y = 175 \end{cases}$$

First, simplify the first equation by dividing all terms by 26:

$$ 2x + y = 275 $$

Step2: Now we have a new system:

$$\begin{cases} 2x + y = 275 \\ x + y = 175 \end{cases}$$

Subtract the second equation from the first equation to eliminate \( y \):

$$ (2x + y) - (x + y) = 275 - 175 $$

$$ 2x + y - x - y = 100 $$

$$ x = 100 $$

Step3: Substitute \( x = 100 \) into the second equation \( x + y = 175 \):

$$ 100 + y = 175 $$

Subtract 100 from both sides:

$$ y = 175 - 100 $$

$$ y = 75 $$

Answer:

\( x = 100 \), \( y = 75 \)