Question

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???

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's represent the cost for each company as a system of equations:

Let x be the number of balloons ordered and y be the total cost.

For Balloon Express:
2x + 10 = y

For Balloon Mania:
1.5x + 20 = y

We know that the O'Donnells plan to order 30 balloons, so x = 30.

Now we can plug in x = 30 into both equations to find the total cost for each company:

For Balloon Express:
2(30) + 10 = 60 + 10 = 70

For Balloon Mania:
1.5(30) + 20 = 45 + 20 = 65

Therefore, the O'Donnells should choose Balloon Mania as it will cost them $65, saving $5 compared to Balloon Express.

Answer 2

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?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's represent the costs and revenue in terms of a system of equations:

Let x be the number of quiches sold.

The cost for making x quiches will be:
C(x) = 30 + 0.50x

The revenue from selling x quiches will be:
R(x) = 2x

The Spanish Club wants to break even, which means that the cost equals the revenue. So we set up the equation:
C(x) = R(x)

30 + 0.50x = 2x

Now, we solve for x:
30 = 2x - 0.50x
30 = 1.50x
x = 30 / 1.50
x = 20

Therefore, the Spanish Club will need to sell 20 quiches in order to break even.

Answer 4

The Baynard High School Boosters are selling hot dogs and pretzels at the concession stand. They have 300 hot dogs and pretzels in stock and want to earn an income of $800. They plan to sell the hot dogs for $4 each and the pretzels for $2 each. How many hot dogs and how many pretzels do the boosters need to sell to reach their goal of $800?

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's represent the number of hot dogs as "x" and the number of pretzels as "y".

The boosters want to earn $800, so the total income can be represented as: 4x + 2y = 800

They have a total of 300 hot dogs and pretzels in stock, so the total number of items can be represented as: x + y = 300

We can solve this system of equations using substitution. First, solve for x in terms of y in the second equation:

x = 300 - y

Now substitute this expression for x in the first equation:

4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200

Now that we have the value for y, we can find the value for x using x = 300 - y:

x = 300 - 200
x = 100

Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.