Maths-
General
Easy
Question
Chocolate costs $7 a pound. Biscuits cost $9 a pound. There is a mixture of peanuts and cashews that weighs 10pounds and costs $84. How many pounds of chocolates are there in the mixture?
Hint:
let the weight of chocolate be x (Pounds) and the weight of biscuits be y(Pounds).
Given total weight = weight of chocolates + weight of biscuits = 10(Pounds)
Given total cost of 10 pound mixture = cost of x pounds chocolate + cost of y pounds Biscuits = $94.
The correct answer is: 10 pounds.
Ans :- weight of chocolate is 3 (Pounds) in the mixture of chocolates and biscuits of 10 pounds.
Explanation :-
Chocolate cost $7 a pound. Biscuits cost $9 a pound
Step 1:- frame the system of linear equations with given conditions.
let the weight of chocolate be x (Pounds) and the weight of biscuits be y(Pounds).
Given total weight = weight of chocolates + weight of biscuits = 10(Pounds)
x + y = 10 — eq1
Given total cost of 10 pound mixture = cost of x pounds chocolate + cost of y pounds Biscuits = $94.
Cost of x pounds chocolate = x 
cost of chocolate for 1 pound( = $7 given)
Cost of x pounds chocolate = x $7 = 7x(in $)
Cost of y pounds of biscuits = y cost of biscuits for 1 pound (= $9 given )
Cost of y pounds of biscuits = y $9 = 9y (in $)
So total cost of 10 pounds mixture = 
— eq2
Step 2:- eliminate the x and find y
Doing eq2 - 3(eq1) to eliminate x .
∴y = 7
Step 3:- find x by substituting the value of y in eq1.
∴x = 3
∴weight of chocolate is 3 (Pounds) in the mixture of chocolates and biscuits of 10 pounds.
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