Question

The Jackson Jammers are giving away bags and caps at their next game. The bags, b , cost them $10 each, and the caps, c , cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.(1 point) Responses b+c=2,000; 5b+10c=12,500 b plus c equals 2,000 ; 10 b plus 10 c equals 12,500 b+c=2,000; 10b+5c=12,500 b plus c equals 2,000 ; 10 b plus 5 c equals 12,500 b+c=12,500; 5b+10c=2,000 b plus c equals 12,500 ; 5 b plus 10 c equals 2,000 b+c=12,500; 10b+5c=2,000

Answer 1

To model the situation with the Jackson Jammers, we need to create two linear equations based on the information provided.

1. The first equation accounts for the total number of items. The total number of bags (b) and caps (c) combined should equal 2,000: \[ b + c = 2000 \]

2. The second equation addresses the budget. The bags cost $10 each, and the caps cost $5 each. The total cost must not exceed their budget of $12,500: \[ 10b + 5c = 12500 \]

Thus, the pair of linear equations that model this situation is: \[ \begin{align*} b + c &= 2000 \ 10b + 5c &= 12500 \end{align*} \]

From your provided response options, the correct equations are represented as:

• b + c = 2000; 10b + 5c = 12,500

Answer 2

Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son, and they plan to have a clown bring balloons to the party. Balloon Express charges $2 per balloon and $10 for delivery. Balloon Mania charges $1.50 per balloon and $20 for delivery. If the O’Donnells plan to order 30 balloons, which company should they choose, and how much will they save?(1 point) Responses Balloon Express; $25 Balloon Express; $25 Balloon Express; $5 Balloon Express; $5 Balloon Mania; $25 Balloon Mania; $25 Balloon Mania; $5

Answer 3

To determine which balloon company the O’Donnells should choose, we can set up equations to calculate the total cost for each company based on the number of balloons they want to order (30 balloons).

Cost for Balloon Express:

• Cost per balloon: $2
• Delivery fee: $10

The total cost for Balloon Express can be calculated as follows: \[ \text{Cost}{\text{Express}} = (2 \text{ per balloon} \times 30 \text{ balloons}) + 10 \text{ delivery fee} \] \[ \text{Cost}{\text{Express}} = (2 \times 30) + 10 = 60 + 10 = 70 \]

Cost for Balloon Mania:

• Cost per balloon: $1.50
• Delivery fee: $20

The total cost for Balloon Mania can be calculated as follows: \[ \text{Cost}{\text{Mania}} = (1.50 \text{ per balloon} \times 30 \text{ balloons}) + 20 \text{ delivery fee} \] \[ \text{Cost}{\text{Mania}} = (1.50 \times 30) + 20 = 45 + 20 = 65 \]

Comparing the costs:

• Total cost for Balloon Express: $70
• Total cost for Balloon Mania: $65

Now, to determine which company is cheaper and how much they would save: \[ \text{Savings} = \text{Cost}{\text{Express}} - \text{Cost}{\text{Mania}} = 70 - 65 = 5 \]

Conclusion:

The O'Donnells should choose Balloon Mania, and they will save $5 compared to Balloon Express.

Thus the final choice is:

• Balloon Mania; $5

Answer 4

The Spanish Club at Santa Fe Middle School wants to sell mini quiches to raise money for a field trip. The culinary department at their school will make the quiches for $30 plus $0.50 per quiche for the ingredients. The Spanish Club wants to sell each quiche for $2. How many quiches will they need to sell in order to break even?(1 point) Responses 75 quiches 75 quiches 20 quiches 20 quiches 45 quiches 45 quiches 12 quiches

Answer 5

To find out how many mini quiches the Spanish Club needs to sell in order to break even, we can set up an equation representing the costs and the income from selling the quiches.

Costs:

The total cost to make \( x \) quiches is given by:

• Fixed cost: $30
• Variable cost: $0.50 per quiche

Thus, the total cost can be expressed as: \[ \text{Total Cost} = 30 + 0.50x \]

Revenue:

The revenue from selling \( x \) quiches at $2 each is: \[ \text{Total Revenue} = 2x \]

Break Even Point:

To break even, the total cost must equal the total revenue: \[ 30 + 0.50x = 2x \]

Solving the Equation:

1. Rearrange the equation: \[ 30 = 2x - 0.50x \] \[ 30 = 1.5x \]

2. Solve for \( x \): \[ x = \frac{30}{1.5} = 20 \]

Conclusion:

The Spanish Club needs to sell 20 quiches in order to break even.

Therefore, the correct response is:

• 20 quiches

Answer 6

You are trying to guess the code to a puzzle while participating in an escape room. There are two buttons, blue and red, and you have to put the correct number in each one to unlock the door to the next room. There are only two clues to help you: Clue 1: If you double the blue number and add it to the red number, you get 6. Clue 2: If you quadruple the blue number and add it to double the red number, you get 12. You only get two attempts at the puzzle, and if you get it wrong, the game will be over. Use the system of equations shown to determine how many solutions there are to this puzzle. {2b+r=64b+2r=12 (1 point) Responses There are infinitely many solutions. There are infinitely many solutions. There is no solution. There is no solution. There is only one solution. There is only one solution. There are only two solutions. There are only two solutions.

Answer 7

To solve the puzzle, we can start by translating the given clues into a system of linear equations.

Translating the Clues into Equations:

1. Clue 1: If you double the blue number (let's call it \( b \)) and add it to the red number (let's call it \( r \)), you get 6. \[ 2b + r = 6 \quad \text{(Equation 1)} \]

2. Clue 2: If you quadruple the blue number and add it to double the red number, you get 12. \[ 4b + 2r = 12 \quad \text{(Equation 2)} \]

Simplifying Equation 2:

Next, we can simplify Equation 2. We can divide everything in Equation 2 by 2: \[ 2b + r = 6 \quad \text{(Equation 2 simplified)} \]

Analyzing the Equations:

Now we can see that both equations are:

1. \( 2b + r = 6 \) (from Equation 1)
2. \( 2b + r = 6 \) (from the simplified Equation 2)

Since both equations are identical, they represent the same line in a two-dimensional plane.

Conclusion on Solutions:

1. Identical equations mean infinitely many solutions. Any value of \( b \) that satisfies \( r = 6 - 2b \) will provide a corresponding value for \( r \), resulting in an infinite number of \( (b, r) \) pairs that satisfy both conditions.

Thus, the answer is:

• There are infinitely many solutions.

Answer 8

Use the chemical reaction to answer the question. ​CaCO3→CO2​+CaO A scientist heats 30 grams of calcium carbonate ( CaCO3 ) in the chemical reaction shown. What is the total mass of the products? (1 point) Responses 30 grams 30 grams 10 grams 10 grams 60 grams 60 grams 15 grams

Answer 9

In a chemical reaction, the Law of Conservation of Mass states that the total mass of the reactants must equal the total mass of the products. This means that if a scientist starts with 30 grams of calcium carbonate (CaCO₃), the total mass of the products will also be 30 grams, regardless of how the mass is distributed among the products.

In the given reaction:

\[ \text{CaCO}_3 \rightarrow \text{CO}_2 + \text{CaO} \]

the products of the reaction are carbon dioxide (CO₂) and calcium oxide (CaO).

Since the total mass of the reactants (30 grams of CaCO₃) equals the total mass of the products, we can definitively conclude that the total mass of the products will be:

• 30 grams

Thus, the correct response is:

• 30 grams

Answer 10

Use the chemical reaction to answer the question. 4​Fe+3O2→2Fe2O3​ What happens to atoms of Fe and O2 during the reaction? (1 point) Responses They are lost. They are lost. They are rearranged. They are rearranged. They maintain their properties. They maintain their properties. They gain mass.

Answer 11

In a chemical reaction, atoms are neither created nor destroyed; instead, they are rearranged to form new substances. In the reaction:

\[ 4 \text{Fe} + 3 \text{O}_2 \rightarrow 2 \text{Fe}_2\text{O}_3 \]

the iron (Fe) and oxygen (O₂) atoms are combined in specific ratios to form iron(III) oxide (Fe₂O₃).

Analysis of the Options:

1. They are lost. — This is incorrect because atoms are not lost in a chemical reaction.
2. They are rearranged. — This is correct. During the reaction, the Fe and O₂ atoms are rearranged to form Fe₂O₃.
3. They maintain their properties. — This is misleading as the properties of the elements change when they form a compound.
4. They gain mass. — This is incorrect in the context of the reaction; mass is conserved, not gained.

Conclusion:

The correct response is:

• They are rearranged.