Fiona bought some packets of pencils, pens and erasers in the ratio 5:3:2 respectively. There were 12 pencils, 8 pens and 7 erasers in each packet. If she bought 296 pencils and
erasers, how many pens did she buy?
12x+7y = 296
x/y = 5/2
so, 20 packs of pencils and 8 packs of erasers
5:3:2 = 20:12:8
so 12 packs of pens = 96 pens
To find the number of pens Fiona bought, we need to determine the number of packets she bought and then calculate the number of pens in those packets.
Let's first find the total number of packets Fiona bought by finding the least common multiple (LCM) of the ratios for pencils, pens, and erasers.
The ratio of pencils to pens to erasers is 5:3:2.
The LCM of 5, 3, and 2 is 30.
So, Fiona bought 30 packets.
Now, let's calculate the number of pens in those packets.
Since there were 8 pens in each packet, we multiply the number of packets by the number of pens per packet:
30 packets * 8 pens/packet = 240 pens.
Therefore, Fiona bought 240 pens.
To find out how many pens Fiona bought, we first need to determine the total number of packets she purchased.
Let's consider the ratio of pencils, pens, and erasers: 5:3:2. This means that for every 5 units of pencils, Fiona purchased 3 units of pens and 2 units of erasers.
Since each packet contains 12 pencils, we can calculate the number of packets for pencils by dividing the total number of pencils by the number of pencils in each packet:
Total number of packets for pencils = 296 pencils ÷ 12 pencils/packet
Similarly, since each packet contains 7 erasers, we can calculate the number of packets for erasers by dividing the total number of erasers by the number of erasers in each packet:
Total number of packets for erasers = 296 erasers ÷ 7 erasers/packet
Since the ratio of pencils to pens is 5:3, we can deduce that the ratio of packets for pencils to pens is also 5:3. Therefore, the number of packets for pens is the same as the number of packets for pencils.
So, to find out the number of packets for pens, we subtract the total number of packets for pencils and erasers from the total number of packets Fiona purchased:
Total number of packets for pens = Total number of packets - (Total number of packets for pencils + Total number of packets for erasers)
Now we can calculate how many pens Fiona bought by multiplying the number of packets for pens by the number of pens in each packet:
Number of pens = Total number of packets for pens x 8 pens/packet
To summarize, to find out how many pens Fiona bought:
1. Calculate the total number of packets for pencils: 296 pencils ÷ 12 pencils/packet
2. Calculate the total number of packets for erasers: 296 erasers ÷ 7 erasers/packet
3. Calculate the total number of packets for pens: Total number of packets - (Total number of packets for pencils + Total number of packets for erasers)
4. Multiply the total number of packets for pens by 8 pens/packet to find the number of pens Fiona bought.