Maths-
General
Easy

Question

Candies  cost $2 an ounce and have 500 calories in an ounce. Cookies cost $3 an ounce and have 400calories in an ounce. A mixture of candies and cookies costs $29 and has 4,800 calories. Create a system of equations to model this scenario. How many ounces of candies are there in the mixture?

Hint:

candies  cost $2 an ounce and have 500 calories in an ounce. Cookies cost $3 an ounce and have 400calories in an ounce.
Let the no. of ounces of candy be x and no. of ounces of cookies be y
Total cost = cost of x ounces candy + cost of y ounces cookies =  $29
Total no. of calories = calories in x ounces candy + calories in y ounces cookies  = 4,800

The correct answer is: 4 ounces.


    Ans :-The no. of ounces of candy is 4 ounces in the mixture .
    Explanation :-
    Given ,candies  cost $2 an ounce and have 500 calories in an ounce. Cookies cost $3 an ounce and have 400calories in an ounce.
    Step 1:Frame the system of linear equations based on given conditions
    Let the no. of ounces of candy be x and no. of ounces of cookies be y
    Total cost = cost of x ounces candy + cost of y ounces cookies =
    cross timescost of each ounce candy + y cross times cost of each ounce cookies = $29
    not stretchy rightwards double arrow x space cross times space straight $ 2 plus y space cross times space straight $ 3 equals straight $ 29 not stretchy rightwards double arrow 2 x plus 3 y equals 29— Eq1
    Total no. of calories = calories in x ounces candy + calories in y ounces cookies =
    cross timescalories in each ounce candy + y cross timescalories in each ounce cookies = 4,800
    not stretchy rightwards double arrow x space cross times space 500 plus y space cross times space 400 equals 4 comma 800 not stretchy rightwards double arrow 5 x plus 4 y equals 48 — Eq2
    Step 2:- eliminate x to find the value of y .
    Doing 5(Eq1) -2(Eq2)  to eliminate x .
    5 left parenthesis 2 x plus 3 y right parenthesis minus 2 left parenthesis 5 x plus 4 y right parenthesis equals 5 left parenthesis 29 right parenthesis minus 2 left parenthesis 48 right parenthesis
    10 x minus 10 x plus 15 y minus 8 y equals 145 minus 96
    7 y equals 49
    ∴y = 7
    Step 3:- find x by substituting the value of y in eq1.
    2 x plus 3 y equals 29 not stretchy rightwards double arrow 2 x plus 21 equals 29
    not stretchy rightwards double arrow 2 x equals 29 minus 21 equals 8
    ∴x =4
    ∴ we get the no. of ounces of candy be x = 4 ounces.

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