... find the no.of each type of coins
Responses (1)
The abbreviation for the Indian rupee according to the ISO-4217-code is INR.
[0] 1 INR = 100 paise
There are two unknowns x, y:
x = number of coins with the value of 10 paise each.
y = number of coins with the value of 50 paise each.
1st condition:
[1] x + y = 70
2nd condition:
The values of these 70 coins add up to 19 INR (19 INR = 1900 paise [0]).
[2] 10x + 50y = 1900
We have to solve this system of linear equations:
[3]:=([1] * 10) -> 10x + 10y = 700
[4]:=([2] - [3]) -> 40y = 1200 ;;divide by 40 to get y:
[5] y = 30
Insert this value of y into [2]:
[6]:=([2]<-[5]) -> 10x + 1500 = 1900 ;;divide by 10:
x + 150 = 190 ;;isolate x:
[7] x = 40
Verify:
[8]:=([1]<-[7, 5]) -> 40 + 30 = 70 ;; O.K.
[9]:=([2]<-(7, 5]) -> 400 + 1500 = 1900 ;;O.K.
And 1900 paise = 19 INR [0].
CORRECTION:
Equation [9] should read:
[9]:=([2]<-[7, 5]) -> 400 + 1500 = 1900 ;;O.K.
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As AN ASIDE:
Maybe this word problem is a catch question. Wikipedia tells me that "as of 2011 only 50 paise coins are legal tender".
(https://en.wikipedia.org/wiki/Indian_rupee)
If that's right, then 38 coins á 50 paise alone account for the 19 INR and 32 coins á 10 paise with no actual value have to be added just to meet the first condition.