Answer :
The exact amount of money in his bank is $ 1.8.
What is unitary method?
- The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.
- Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.
- Recognizing the units and values is crucial when using the unitary technique to a problem.
- Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.
acc to our question=
- 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 2.0
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