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 =

x cost of each ounce candy + y cost of each ounce cookies = $29

— Eq1

Total no. of calories = calories in x ounces candy + calories in y ounces cookies =

x calories in each ounce candy + y calories in each ounce cookies = 4,800

— Eq2

Step 2:- eliminate x to find the value of y .

Doing 5(Eq1) -2(Eq2) to eliminate x .

∴y = 7

Step 3:- find x by substituting the value of y in eq1.

∴x =4

∴ we get the no. of ounces of candy be x = 4 ounces.

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We could also calculate the standard deviation for both the data sets

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= terms given in the data

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After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.