Question

A certain fruit salad sold apples for $ Rs.0.70 $ each and bananas for $Rs. 0.50 $ each. If a customer purchased both apples and bananas from the stand for a total of $Rs. 6.30 $, what total number of apples and bananas did the customer purchase?
 $
  {\text{A}}{\text{. 10}} \\
  {\text{B}}{\text{. 11}} \\
  {\text{C}}{\text{. 12}} \\
  {\text{D}}{\text{. 13}} \\
  {\text{E}}{\text{. 14}} \\
  $

Answer 1

Hint: Equality is the general relationship between two or more quantities. It basically tells the changes occurred when any of the quantity is changed.
In this question, we have been asked for the summation of the number of apples and the number of bananas that the customer bought by paying an amount of $Rs. 6.30 $. For this, we need to first derive an equation that will illustrate the relation between the cost price of the fruits for the customer.

Complete step-by-step answer:
Let the number of apples that the customer bought be $ x $ .
Let the number of bananas that the customer bought be $ y $ .
As the price of one apple is $Rs. 0.70 $ then, the total price of the apples that the customer bought will be calculated by multiplying the total number of apples and cost per apple is:
$ {C_a} = 0.70x $
Similarly, the price of one banana is $Rs. 0.50 $ then, the total price of the bananas that the customer bought will be calculated by multiplying the total number of bananas and cost per banana as: $ {C_b} = 0.50y $
According to the question, the total cost to the customer when he bought $ x $ apples and $ y $ bananas is $Rs. 6.30 $. So, we can write it as:
 $
\Rightarrow {C_a} + {C_b} = 6.30 \\
\Rightarrow 0.70x + 0.50y = 6.30 \\
\Rightarrow 7x + 5y = 63 \\
  $
Now, after carefully observing the above equation, we can see that $ x $ and $ y $ should be such that the equation $ 7x + 5y = 63 $ holds true.
To solve this type of equation where two variables are present but no other equation is available; the trial and error method is the only option that we opt for.
The equation $ 7x + 5y = 63 $ can also be written as $ y = \dfrac{{63 - 7x}}{5} $ .
It is also clear that the value $ y $ cannot be in decimals and it should be a whole number so, the value of $ y $ could be 1,2,3,4,.. and so on.
Now, calculate the value of $ y $ for different values of $ x $ so that the value of $ x $ should also be a whole number.
For $ x = 1 $ :
 $ \Rightarrow y = \dfrac{{63 - 7}}{5} = \dfrac{{56}}{5} = 11.2 $
For $ x = 2 $ :
 $
\Rightarrow y = \dfrac{{63 - (7 \times 2)}}{5} \\
   = \dfrac{{63 - 14}}{5} = \dfrac{{49}}{5} \\
   = 9.8 \\
  $
For $ x = 3 $ :
 $
\Rightarrow y = \dfrac{{63 - (7 \times 3)}}{5} \\
   = \dfrac{{63 - 21}}{5} = \dfrac{{42}}{5} \\
   = 8.4 \\
  $
For $ x = 4 $ :
 $
\Rightarrow y = \dfrac{{63 - (7 \times 4)}}{5} \\
   = \dfrac{{63 - 28}}{5} = \dfrac{{35}}{5} \\
   = 7 \\
  $
For the value of $ x $ as 4, the value of $ y $ is 7 and both are now a whole number.
Hence, the number of apples and the bananas that the customer bought is 4 and 7 respectively.
The total number of apples and bananas that the customer bought is $ 7 + 4 = 11 $

Note: The quantity of fruits cannot be in decimal and it should be in whole numbers only. Here, only one equation is given with two variables and we need to investigate the numbers by trial and error method only.