A person spent ₹564 in buying geese and ducks,if each cost ₹7 and each duck ₹3 and if the total number of birds bought was 108,how many of each type did he buy?
please solve this question
Answers
Step-by-step explanation:
Given:-
A person spent ₹564 in buying geese and ducks,if each cost ₹7 and each duck ₹3 and if the total number of birds bought was 108.
To find:-
How many of each type did he buy?
Solution:-
Let the number of geese be X
and the number of ducks be Y
The cost of each geese=₹ 7
Total cost of X geese=₹7X
The cost of each duck=₹3
Total cost of Y ducks=₹3Y
The cost of all geese and duck=₹564
=>7X+3Y=564.........(1)
Total no. of birds=X+Y
According to the problem ,
Total no. of birds was bought=108
X+Y=108.......(2)
Multiplying equation (2) with 7 then
7X+7Y=756.......(3)
from (1)&(3)
7X+7Y = 756
7X+3Y = 564
(-)
___________
0+4Y=192
___________
=>4Y=192
=>Y=192/4
=>Y=48
from(2)
X+48=108
=>X=108-48
=>X=60
there fore,X=60 and Y=48
Solution:-
He bought the birds
No. of geese =60
No.Of duck=48
Check:-
geese+duck=60+48=108
Total birds are108
cost of 60 geese=7×60=₹420
No.Of 48 duck=3×48=₹144
Total cost =₹420+₹144=₹564
Given relations are verified.
Used method:-
Elimination method in pair of linear equations in two variables.
Answer:
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