Emily has a total of two hundred eight-two pennies, nickels, and quarters. She has three and a half times as many pennies as quarters and one-fifth as many nickels as quarters and one-fifth as many nickels as quarters. How many of each coin does she have?
Given,
Total Number of coins= 282
Let the number of pennies be x.
Let the number of quarters be y.
Let the number of nickels be z.
Therefore,
x+y+z= 282
According to given,
Number of quarters= 3.5 times as many as pennies
y= 3.5x
Also given,
Number of quarters=(1/5) times as many as nickles
y= z*(1/5)
z= 5y=(3.5x)*5= 17.5x
Therefore,
x+(3.5x)+(17.5x)= 282
22x= 282
x= 12.81818181818
y= 3.5*12.81818181818
y= 44.86363636363
z= 17.5*12.81818181818
z=224.31818181815
Therefore,
the number of pennies=12.81818181818= 13
the number of quarters=44.86363636363= 45
the number of nickels=224.31818181815= 224
+36916 q = # quarters
p = # of pennies = 3.5 q
n = # nickels = 1/5 q summed they equal 282
q + 3.5 q + 1/5 q = 282
4.7 q = 282
q = 60 then p = 210 n = 12
