Question

show all the work to get full credit.

1. peter has $100 to spend on drinks for his party. bottles of lemonade cost $2 each, and juice boxes cost $0.50 each. if x is the number of bottles of lemonade and y is the number of juice boxes, which inequality models this situation?
2. ( 0.50x + 2y leq 100 )
3. ( 2x + 0.50y leq 100 )
4. ( 0.50x + 2y geq 100 )
5. ( 2x + 0.50y geq 100 )
6. given the system of equations: ( y + 4x = 5 )( 2x - 3y = 10 )

a step in solving this system by using the substitution method would be
(1) ( 2(5 - 4x) + 4x = 5 )
(3) ( 2x - 3(5 - 4x) = 10 )
(2) ( 2(5 + 4x) + 4x = 5 )
(4) ( 2x - 3(5 + 4x) = 10 )

1. the celluloid cinema sold 150 tickets to a movie. some of these were child tickets and the rest were adult tickets. a child ticket cost $7.75 and an adult ticket cost $10.25. if the cinema sold $1470 worth of tickets, write a system of equations that could represent the situation? introduce the variable.
2. solve the inequality below: ( 1.8 - 0.4y geq 2.2 - 2y )
3. anna plans to spend $30 on balloons and party hats for her daughters birthday party, including tax, balloons cost $2 each and party hats cost $1.50 each. the number of party hats anna needs is twice as many as the number of balloons.

Explanation:

Question 1

Step1: Calculate the cost of lemonade and juice boxes

The cost of \(x\) bottles of lemonade is \(2x\) dollars (since each bottle is \(\$2\)), and the cost of \(y\) juice - boxes is \(0.5y\) dollars (since each juice - box is \(\$0.5\)).

Step2: Set up the inequality based on the total money available

Peter has at most \(\$100\) to spend. So the sum of the costs of lemonade and juice boxes must be less than or equal to \(100\). The inequality is \(2x + 0.5y\leq100\)

Step1: Solve the first equation for \(y\)

From \(y + 4x=5\), we get \(y = 5-4x\)

Step2: Substitute \(y = 5 - 4x\) into the second equation

Substitute \(y\) in \(2x-3y = 10\). We get \(2x-3(5 - 4x)=10\)

Step1: Define the variables

Let \(x\) be the number of child tickets and \(y\) be the number of adult tickets.

Step2: Set up the first equation based on the number of tickets

The total number of tickets sold is \(150\). So \(x + y=150\)

Step3: Set up the second equation based on the cost of tickets

The cost of a child ticket is \(\$7.75\) and an adult ticket is \(\$10.25\), and the total money from ticket sales is \(\$1470\). So \(7.75x+10.25y = 1470\)

Answer:

1. \(2x + 0.5y\leq100\)

Question 2