A mother is planning a birthday party for her son and she wants to give each child 15 balloons. There are 50 balloons in each packet she purchases. How many packets of balloons does she need to purchase for a party of 16 children?
A.
5
B.
17
C.
6
D.
50
The Correct Answer and Explanation is:
To determine how many packets of balloons the mother needs to purchase for the party, we should follow these steps:
- Calculate the Total Number of Balloons Needed: Each child is supposed to receive 15 balloons. With 16 children attending the party, the total number of balloons required can be calculated as follows:Total balloons needed=15 balloons/child×16 children\text{Total balloons needed} = 15 \text{ balloons/child} \times 16 \text{ children}Total balloons needed=15 balloons/child×16 children Total balloons needed=240 balloons\text{Total balloons needed} = 240 \text{ balloons}Total balloons needed=240 balloons
- Determine the Number of Balloons per Packet: Each packet contains 50 balloons.
- Calculate the Number of Packets Required: To find out how many packets are needed, divide the total number of balloons by the number of balloons per packet:Number of packets=Total balloons neededBalloons per packet\text{Number of packets} = \frac{\text{Total balloons needed}}{\text{Balloons per packet}}Number of packets=Balloons per packetTotal balloons needed Number of packets=240 balloons50 balloons/packet\text{Number of packets} = \frac{240 \text{ balloons}}{50 \text{ balloons/packet}}Number of packets=50 balloons/packet240 balloons Number of packets=4.8\text{Number of packets} = 4.8Number of packets=4.8Since you cannot purchase a fraction of a packet, you need to round up to the nearest whole number. Therefore, the mother needs to purchase 5 packets to ensure there are enough balloons for every child.
- Confirming the Result:
- If she buys 4 packets: Total balloons from 4 packets=4×50=200 balloons\text{Total balloons from 4 packets} = 4 \times 50 = 200 \text{ balloons}Total balloons from 4 packets=4×50=200 balloons Since 200 balloons are not enough (240 needed), 4 packets will be insufficient.
- If she buys 5 packets: Total balloons from 5 packets=5×50=250 balloons\text{Total balloons from 5 packets} = 5 \times 50 = 250 \text{ balloons}Total balloons from 5 packets=5×50=250 balloons With 250 balloons, there will be enough to cover the 240 needed, with 10 balloons left over.
Therefore, the correct number of packets needed is 5.
Answer: A. 5