Answer:
The number of small balloons = 46
The number of large balloons = 159
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
Step-by-step explanation:
The volume of each small balloon = 300 in.³
The volume of each large balloon = 1000 in.³
The cost of one package of 50 small balloons = $2.59
The cost of one package of 24 large balloons = $1.99
The volume of one small tank of pressurized helium = 20 ft³
The volume cost of one small tank of pressurized helium = $10.49
By conversion
20 ft³ = 34,560 in.³
The volume of 30 small balloons = 30 × 300 in.³ = 9,000 in.³
The volume of 30 large balloons = 30 × 1000 in.³ = 30,000 in.³
The volume taken by 24 large balloons = 24,000 in.³,
24 large balloons cost = $1.99
The volume taken by 50 small balloons = 15,000 in.³
50 small balloons cost = $2.59
Therefore, we buy more large balloons
We have;
A×300 + B×1000 = C×34,560
Given that all the helium will be used, the volume of helium will be a multiple of 300, therefore, when 5 bottles of helium is used, we have;
A×300 + B×1000 = 5×34,560 = 172,800 in.³
Given that there will be at least 30 of each balloon, gives;
We remove the minimum possible quantity (more than 30) of small balloons from 172,800 in.³ leaving multiples of 1,000s as follows;
Using Excel, the quantities of 36 and 46 small balloons give the same cost
For 46 small balloons
The volume of 46 small balloons = 13,800 in.³
Therefore, 172,800 in.³ - 13,800 in.³ = 159,000 in.³ = The volume of the large balloons
The quantity of the large balloons = 159,000 in.³/(1,000 in.³/balloon) = 159 balloons
Therefore, we have 46 small balloons, and 159 large balloons, with 5 small bottles of helium gas
The number of package of large balloons is 159/24 = 6.625 ≈ 7 packages
The cost of the 7 packages of large balloons = 7 × $1.99 = $13.93
The number of package of small balloons is 46/50= 0.92 ≈ 1 package
The cost of the 1 packages of small balloons = 1 × $2.59 = $2.59
The cost of the five bottles of helium = 5 × $10.49 = $52.45
$68.97
The number of small balloons = 46
The number of large balloons = 159
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
At the same cost, we can also have;
The number of small balloons = 36
The number of large balloons = 162
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
Therefore, we can have 36 or 46 small balloons and 162 or 159 large balloons along with 5 bottles of helium gas with a total cost of $13.93 + $2.59 + $52.45 = $68.97.
(Imagine a rectangle with the circumfrence of the base as one side and the height as the other being folded around)
(Plus the area of two circles)