The entrance fees to the Science centre is as follows:

Adult :$ 10 Child :$7
A group package of 1 adult and 2 children can be bought at a discounted price of $21.
One day, 234 adults and 456 children visited the Science Centre. What is the minimum amount of entrance fees that the Science Centre can collect on the day?

456 / 2 = 228

( 228 Adult + 456 Child ) * 21 $ =

228 * 21 $ = 4,788 $

234 Adult - 228 Adult = 6 Adult

6 Adult * 10 $ = 60 $

4,788 $ + 60 $ = 4,848 $

thanks

To find the minimum amount of entrance fees that the Science Centre can collect on the day, we need to consider the different combinations of adults and children visiting the Centre.

First, let's calculate the number of groups that can be formed using the given discounted package. Since the package consists of 1 adult and 2 children, we can check how many 1 adult + 2 children groups can be formed with the total number of adults and children.

To calculate the number of groups, we need to find the minimum of two values:
1. The number of adults divided by 1 (as 1 adult is required for each group).
2. The number of children divided by 2 (as 2 children are required for each group).

Number of 1 adult + 2 children groups = Min(234 adults / 1 adult per group, 456 children / 2 children per group)

Number of groups = Min(234, 228) = 228

Now, let's calculate the number of remaining adults and children after forming all possible groups.

Remaining adults = Total adults - (Number of groups * 1 adult per group)
Remaining adults = 234 - (228 * 1)
Remaining adults = 6

Remaining children = Total children - (Number of groups * 2 children per group)
Remaining children = 456 - (228 * 2)
Remaining children = 456 - 456
Remaining children = 0

Now, we can calculate the minimum amount of entrance fees by considering the groups and the remaining individuals.

Total entrance fees collected from groups = Number of groups * Discounted package price
Total entrance fees collected from groups = 228 groups * $21 per group
Total entrance fees collected from groups = $4796

Total entrance fees collected from remaining individuals (6 adults) = 6 adults * $10 per adult
Total entrance fees collected from remaining individuals = $60

Hence, the minimum amount of entrance fees that the Science Centre can collect on the day is $4796 + $60 = $4856.