Chapter 6.5, Problem 4P

To determine

To find: To set a linear inequality on modeling given situation and then finding three possible combinations of peanuts and cashews, one can buy.

Answer to Problem 4P

Three possible combinations of peanuts and cashews are,

1. 3 lb peanuts and 1 lb cashew
2. 1 lb peanuts and 2 lb cashew
3. 4 lb peanuts and 1 lb cashew

Explanation of Solution

Given information: Peanuts cost $2/lb and Cashews cost $4/lb and one can not spend more than $12 on nut.

Concept used: First set the linear inequality, representing given situation using following statement,

  $\text{Amount of peanuts}\times \text{its cost+amount of cashews }\times \text{its cost}\le \text{12}$

And then find three values of unknown variables, satisfying this inequality.

Calculation: Let x lb of peanuts and y lb of cashews are bought. So, use above statement to form linear inequality as,

  $2x+4y\le 12$

So, different combinations of x and y values, satisfying above inequality may be,

  $\begin{array}{l}(i)x=3,y=1\\ (ii)x=1,y=2\\ (iii)x=4,y=1\end{array}$

Conclusion: So, different possibility of buying may be,

1. 3 lb peanuts and 1 lb cashew
2. 1 lb peanuts and 2 lb cashew
3. 4 lb peanuts and 1 lb cashew