Question

1. andre wants to purchase some onions and tomatoes to make tomato soup for a large event. he looks at two different recipes. one of the recipes for tomato soup states that 4 times the number of tomatoes, x, plus 5 times the number of onions, y, should produce 109 bowls of tomato soup. the other recipe for tomato soup states that 2 times the number of tomatoes used minus the number of onions used should produce 23 bowls of tomato soup. create a system of equations representing the two recipes. how many tomatoes and onions will andre need to purchase to satisfy both recipes? 12 tomatoes 10 onions 16 tomatoes 9 onions 22 tomatoes 6 onions 18 tomatoes 8 onions 21) the school drama club is organizing an event at the local community theater. it costs $325.00 plus $35.00 per seat to rent the theater. if the drama club sells tickets to their production for $40.00 each, they will break even as long as they sell out every seat. how many seats are in the theater? write and solve an equation to determine how many seats are in the theater. 40 seats 55 seats 65 seats 80 seats

Explanation:

Question 20

Step1: Define variables and set up equations

Let \( x \) be the number of tomatoes and \( y \) be the number of onions.
From the first recipe: \( 4x + 5y = 109 \)
From the second recipe: \( 2x - y = 23 \)

Step2: Solve the system of equations

We can use the substitution or elimination method. Let's use elimination. Multiply the second equation by 5: \( 10x - 5y = 115 \)
Now add this to the first equation: \( (4x + 5y) + (10x - 5y) = 109 + 115 \)
Simplify: \( 14x = 224 \)
Solve for \( x \): \( x = \frac{224}{14} = 16 \)
Substitute \( x = 16 \) into the second equation: \( 2(16) - y = 23 \)
\( 32 - y = 23 \)
Solve for \( y \): \( y = 32 - 23 = 9 \)

Step1: Define variable and set up equation

Let \( x \) be the number of seats.
The cost to rent the theater is \( 325 + 35x \)
The revenue from selling tickets is \( 40x \)
At break - even, cost = revenue, so \( 325+35x = 40x \)

Step2: Solve the equation

Subtract \( 35x \) from both sides: \( 325=40x - 35x \)
Simplify: \( 325 = 5x \)
Solve for \( x \): \( x=\frac{325}{5}=65 \)

Answer:

16 tomatoes, 9 onions (corresponding to the option: 16 tomatoes, 9 onions)

Question 21