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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Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

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

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

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

Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

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

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

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