Let's define two variables:
- Let x be the number of balloons ordered from Balloon Express.
- Let y be the number of balloons ordered from Balloon Mania.
We can set up the following equations based on the given information:
1) Balloon Express charges $2 per balloon and $10 for delivery:
2x + 10 = total cost for Balloon Express
2) Balloon Mania charges $1.50 per balloon and $20 for delivery:
1.5y + 20 = total cost for Balloon Mania
We know that the O'Donnells plan to order 30 balloons, therefore x + y = 30.
We can solve this system of equations to determine which company the O'Donnells should choose and how much they will save.
Let's solve it:
From equation 1: 2x + 10 = total cost for Balloon Express --> (equation 3)
From equation 2: 1.5y + 20 = total cost for Balloon Mania --> (equation 4)
From equation 3, solve for x:
2x + 10 = total cost for Balloon Express
2x = total cost for Balloon Express - 10
x = (total cost for Balloon Express - 10)/2
From equation 4, solve for y:
1.5y + 20 = total cost for Balloon Mania
1.5y = total cost for Balloon Mania - 20
y = (total cost for Balloon Mania - 20)/1.5
Now, substitute x + y = 30 into the equations for x and y:
(total cost for Balloon Express - 10)/2 + (total cost for Balloon Mania - 20)/1.5 = 30
Multiply through by 2 to get rid of the fraction:
total cost for Balloon Express - 10 + 2(total cost for Balloon Mania - 20)/1.5 = 60
total cost for Balloon Express - 10 + 4(total cost for Balloon Mania - 20)/3 = 60
total cost for Balloon Express - 10 + 4(total cost for Balloon Mania - 20) = 180
total cost for Balloon Express - 10 + 4 * total cost for Balloon Mania - 80 = 180
total cost for Balloon Express + 4 * total cost for Balloon Mania - 90 = 180
Combine like terms:
5 * total cost for Balloon Mania = 270
Solve for total cost for Balloon Mania:
total cost for Balloon Mania = 270 / 5 = $54
Now substitute this value into equation 3 to solve for total cost for Balloon Express:
total cost for Balloon Express = 2 * x + 10 = 2 * (30 - y) + 10 = 2 * (30 - 54) + 10 = 2 * (-24) + 10 = -48 + 10 = $-38
Based on the calculations, the O'Donnells should choose Balloon Mania since the total cost for Balloon Mania is $54, compared to a negative cost with Balloon Express.
To find how much they will save, we calculate the difference in total costs:
Amount saved = total cost for Balloon Express - total cost for Balloon Mania
Amount saved = $-38 - $54 = -$92
Therefore, the O'Donnells will save $92 by choosing Balloon Mania.
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; $5 Balloon Express; $5 Balloon Mania; $25 Balloon Mania; $25 Balloon Mania; $5 Balloon Mania; $5 Balloon Express; $25
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