Let's represent the cost of balloons from Balloon Express as B1 and the cost of delivery as D1. Similarly, let's represent the cost of balloons from Balloon Mania as B2 and the cost of delivery as D2.
According to the given information, we can set up the following system of equations:
B1 + D1 = cost of ordering balloons from Balloon Express
B2 + D2 = cost of ordering balloons from Balloon Mania
Since the O'Donnells plan to order 30 balloons, we also know that:
B1 = 2 * 30 = 60 (balloons cost $2 each at Balloon Express)
B2 = 1.50 * 30 = 45 (balloons cost $1.50 each at Balloon Mania)
Now, let's substitute the values of B1 and B2 into the equations:
60 + D1 = cost of ordering balloons from Balloon Express
45 + D2 = cost of ordering balloons from Balloon Mania
To find which company to choose, we need to compare the total costs of each company. The O'Donnells will choose the company with the lower total cost.
Let's compare the costs:
Balloon Express total cost = 60 + D1
Balloon Mania total cost = 45 + D2
Since the O'Donnells plan to order 30 balloons, let's assume the delivery cost is the same for both companies:
D1 = D2
Therefore, the total costs can be simplified to:
Balloon Express total cost = 60 + D1
Balloon Mania total cost = 45 + D1
To find out which company is cheaper, we need to determine the value of D1.
Let's compare the costs:
60 + D1 < 45 + D1
As D1 is the same for both companies, we can disregard it in our comparison since it does not affect the inequality.
60 < 45
Since 60 is not less than 45, the statement is false. Therefore, Balloon Express is not the cheaper option.
Let's now compare the costs:
60 + D1 > 45 + D1
We can disregard D1 since it does not affect the inequality.
60 > 45
Since 60 is greater than 45, the statement is true. Therefore, Balloon Mania is the cheaper option.
To calculate the savings, we need to subtract the cost of ordering the balloons from Balloon Mania from the cost of ordering balloons from Balloon Express:
60 - 45 = $15
Therefore, the O'Donnells will save $15 by choosing Balloon Mania.
However, none of the given options match the calculated amount. The closest option is:
B. Balloon Mania; $25
Although $25 is not the accurate amount, it is the closest option to the calculated savings of $15.
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?
A. Balloon Express; $5
B. Balloon Mania; $25
C. Balloon Express; $25
D. Balloon Mania; $5
1 answer