5. I have a total of 300 in coins of denomination 1, 2 and 5. The
number of 2 coins is 3 times the number of 5 coins. The total number of
coins is 160. How many coins of each denomination are with me?
Answers
Step-by-step explanation:
Given:-
I have a total of 300 in coins of denomination 1, 2 and 5. The number of 2 coins is 3 times the number of 5 coins. The total number of coins is 160.
To find:-
How many coins of each denomination are with me?
Solution:-
Let the number of 1 rupee coins=X
Number of 2 rupees coins=Y
Number of 5 rupees coins=Z
The number of 2 coins is 3 times the number of 5 rupees coins
=Y=3Z----(1)
Total number of coins=160
=>X+Y+Z=160
=>X+3Z+Z=160
=>X+4Z=160-----(2)
Total money=300
value of 1 rupee coins=Rs. X
value of 2 rupee coins=Rs. 2Y
Value of 5 rupee coins= Rs. 5Z
Total money=X+2Y+5Z=300
=>X+2(3Z)+5Z=300
=>X+6Z+5Z=300
=>X+11Z=300-----(3)
Solving(1)&(2)
X+4Z=160
X+11Z=300
(-)
___________
0-7Z=-140
___________
=>-7Z=-140
=>Z=-140/-7
=>Z=20
from(2)
=>X+4(20)=160
=>X+80=160
=>X=160-80
=>X=80
Given that Y=3Z from(1)
=>Y=3(20)=60
Answer:-
Number of 1 rupee coins=80
Number of 2 rupees coins=60
Number of 5 rupees coins=20
Check:-
Total coins=80+60+20=160
Total money=80(1)+60(2)+20(5)
=>80+120+100
=>300
Let the number of ₹5 coins be x.
Then,
number ₹2 coins = 3x
and, number of ₹1 coins = (160 – 4x) Now,
Value of ₹5 coins = x × 5 = 5x
Value of ₹2 coins = 3x × 2 = 6x
Value of ₹1 coins = (160 – 4x) × 1 = (160 – 4x)
According to the question,
5x + 6x + (160 – 4x) = 300
⇒ 11x + 160 – 4x = 300
⇒ 7x = 140
⇒ x = 140/7
⇒ x = 20
Number of ₹5 coins = x = 20
Number of ₹2 coins = 3x = 60
Number of ₹1 coins = (160 – 4x) = 160 – 80 = 80