Chapter 6, Problem 1MPS

To determine

Solve the problem if it has a solution.

Answer to Problem 1MPS

In $2.10 , we can buy either 3 lemons and 6 limes or 8 lemons and 2 limes.

Explanation of Solution

Given:

For $1 you can buy either five lemons or four limes .If you pay $2.10 for some lemons and limes, find all possibilities for the number of each fruit bought.

Calculation:

Since for $1 , you can buy 5 lemons , so , the price of 1 lemon = $\frac{1}{5}=\$0.20$

Since for $1 , you can buy 4 limes , so , the price of 1 lime = $\frac{1}{4}=\$0.25$

Let the number of lemons purchased = x

Let the number of limes purchased = y

Since x lemons and y limes are purchased in $2.10, the equation is :

  $\begin{array}{l}0.20x+0.25y=2.10\\ \Rightarrow 0.25y=2.10-0.20x\\ \Rightarrow y=-0.8x+8.4\end{array}$

Since the number of lemons and limes must be whole numbers, find such combination in which x starts from 0 and increases by 1 , until y becomes negative.

  

From the graph , the possible values of ( x , y ) for which both are whole numbers :

(3,6) and (8,2)

So, in $2.10 , we can buy either 3 lemons and 6 limes or 8 lemons and 2 limes.