James has pennies, nickles and dimes in his bank. he has more than $1.60 and less than $2.00 in the bank. there are 5 times as many pennies as dimes. there is an equal number of nickels and dimes. what is the exact amount of money in his bank?
Answer:
The exact amount of money in his bank is $ 1.8
Solution:
Let "p" be the number of pennies
Let "d" be the number of dimes
Let "n" be the number of nickels
Given that,
There are 5 times as many pennies as dimes
Number of pennies = 5 times the number of dimes
p = 5d ----------- eqn 1
There is an equal number of nickels and dimes
n = d -------- eqn 2
We know that,
value of 1 dime = 0.10 dollar
value of 1 nickel = 0.05 dollar
value of 1 penny = 0.01 dollar
The total value of coins is:
total value = d(0.10) + n(0.05) + p(0.01)
Substitute eqn 1 and eqn 2
total value = d(0.10) + d(0.05) + 5d(0.01)
total value = 0.2d
Given that he has more than $1.60 and less than $2.00 in the bank
Therefore, 0.2d must be greater than 1.60 and less than 2.00
Try for d = 8
total value = 0.2 x 8 = 1.6
But value must be greater than 1.6
Try for d = 9
total value = 0.2 x 9 = 1.8
Thus 1.8 is greater than 1.60 and less than 2.00
Therefore, the exact amount of money in his bank is $ 1.8