Question

If 6 pounds of nuts that cost 1.20 dollar per pound are mixed with 2 pounds of nuts that cost 1.60 dollar per pound, what is the cost per pound of the mixture?
A) 1.30 dollar
B) 1.80 dollar
C) 1.40 dollar
D) 1.60 dollar

Answer 1

Hint:
The cost of the mixture can be found by first finding out the total cost of the mixture and then dividing the total cost of the mixture with the weight of the mixture. Since we are given the cost per pound in the question, the total cost can be calculated by multiplying the cost per pound with the weight of the nuts.

Complete step by step solution:
Let us label the types of nuts as type A and type B. The type A of nuts is the nuts which cost 1.20 dollar per pound. The type B of nuts is the nuts which cost 1.60 dollar per pound. The weight of the type A nuts is ${w_A}$ and the cost per pound is ${p_A}$. Similarly, the weight of the type B nuts is ${w_B}$ and the cost per pound is ${p_B}$.
${w_A} = $ 6
${p_A} = $ 1.20
${w_B} = $ 2
${p_B} = $ 1.60
We find the total cost of the type A and B nuts by multiplying the weight of the nuts with their respective price per pound. The total cost of type A nuts is represented as ${P_A}$ and the total cost of type B nuts is represented as ${P_B}$.
${P_A} = {p_A}{w_A} = 1.20 \times 6 = $ 7.20
${P_B} = {p_A}{w_A} = 1.60 \times 2 = $ 3.20
The total price of the mixture is the sum of the total prices of type A and type B nuts and the total weight of the mixture is the sum of the weights of the type A and type B of nuts. They are represented as P and w.
P = P$_A$ + P$_B$ = $ 7.20 + 3.20 = 10.40$
w = w$_A$ + w$_B$ = 6 + 2 = 8
The price of the mixture per pound is p. It can be found out by dividing the total cost of the mixture by the total weight of the mixture.
$p = \dfrac{P}{w} = \dfrac{10.40}{8} = $ 1.30
Therefore, the cost of the mixture per pound is 1.30 $.

Hence, the correct answer of the question is option A.

Note:
The same method will be used in questions where two different types of things are mixed and we need to find some resultant property of the mixture. For example, this method can be used to find the concentration of the resulting solution by mixing two or more different solutions of different concentrations.