Question

If 6 pounds of nuts that cost $ \$ 1.20 $ per pound are mixed with 2 pounds of nuts that cost $ \$ 1.60 $ per pound, what is the cost per pound of the mixture?
(a) $ \$ 1.30 $
(b) $ \$ 1.80 $
(c) $ \$ 1.40 $
(d) $ \$ 1.60 $

Answer 1

Hint: Here, we will first calculate the price of 6 pounds nuts and 2 pounds nuts using the unitary method. So, for 6 pounds we get as 1pound cost $ \$ 1.20 $ then how much will it cost for 6 pounds. Similarly, we will find 2 pounds. Then, we will get the total cost by adding both costs. Thus, on dividing it with total pounds of mixture, we will get a cost of 1pound mixture.

Complete step-by-step answer:
Here, we are asked to find the cost of mixture per pound means the cost of 1pound mixture.
So, here we have two types of nuts i.e. 6 pounds of nuts cost $ \$ 1.20 $ per pound and the other one is 2 pounds of nuts with cost $ \$ 1.60 $ per pound.
We will first calculate the overall price of 6pounds nuts. So, we are given a cost of per pound thus by using a unitary method we will calculate the cost of 6pounds. We will get as
 $ \begin{align}
  & 1\,pound=\$ 1.20\\
&6\,pounds=?\\\end{align} $
On solving, we get as
 $ =6\times 1.20=\$ 7.20 $ ………………….(1)
Similarly, we will find a cost for 2 pounds. Using unitary method, we will get as
 $ \begin{align}
  & 1\,pound=\$ 1.60\\
&2\,pounds=?\\\end{align} $
On solving, we get as
 $ =2\times 1.60=\$ 3.20 $ ………………..(2)
The total pounds of nuts we have is equal to $ =6+2=8pounds $
So, total costs of 8 pounds mixture are equal to $ =\$ 7.20+\$ 3.20=\$ 10.40 $
Thus, we have costs of 8 pounds worth of mixture as $ \$ 10.40 $ .
So, we will find the cost of 1pound mixture using a unitary method. We will get as
 $ \begin{align}
& \text{8 pound mixture = }\$\text{10}\text{.40}\\
&\text{1 pound mixture = ?}\\
\end{align} $
On further solving, we get as
 $ =\dfrac{10.40}{8}=1.30 $
Thus, a one-pound mixture costs $ \$ 1.30 $ .
So, the correct answer is “Option A”.

Note: Sometimes students forget to calculate the overall price of 6pounds and 2 pounds because the cost of one pound is given. So, doing this we get an answer as a total 8pounds mixture and total cost as $ 1.20+1.60=\$ 1.80 $ . So, students divide 1.80 to 8pounds mixture to find the cost price of 1pound mixture which will result in the wrong answer. Also, none of the options will match to answer. So, do not make this mistake and read the question carefully while solving.