Question

Ibrahim bought 2 pizzas and 3 burgers. He paid a total of $50 to the shopkeeper. In how many ways can we obtain the prices of these two food items?
Assume the price of each of the items is a natural number.

• A. 8
• B. Infinite
• C. 12
• D. 9

Answer 1

The correct option is A 8

Let the price of the pizza be x.
Let the price of the burger be y.
The required equation is 2x + 3y = 50.

We have to find the number of solutions of (x, y).

In the equation 2x + 3y = 50, 2x is an even number.
50 is also an even number.
So, to satisfy the equation, 3y has to be an even number.

3y can be an even number when:
y = 2 --> 3y = 6
y = 4 --> 3y = 12
y = 6 --> 3y = 18
y = 8 --> 3y = 24
y = 10 --> 3y = 30
y = 12 --> 3y = 36
y = 14 --> 3y = 42
y = 16 --> 3y = 48

y cannot take any furthur values. Let's take y = 18
3y = 54, which make 2x = 50 – 54 = –4
x = –2,
which makes the condition of x and y to be a natural number invalid.

Hence, y can take 8 values.

Let's find the value of x corresponding to y.
If y = 2, x = 22.
If y = 4, x = 19.
If y = 6, x = 16.
If y = 8, x = 13.
If y = 10, x = 10.
If y = 12, x = 7.
If y = 14, x = 4.
If y = 16, x = 1.

Hence, 8 solutions exist for the equation.