In the air talent show in the eve of independence day 90 aircraft (only Sukhoi and Mig - 21) participated, It is known that for everyone hour flight a Sukhoi and a Mig - 21 consume 2 litres and 3 litres of fuel respectively. The price of fuel for Sukhoi is `$10` per litre and price for the fuel of Mog - 21 is `$15` per litre. Thus all the aircrafts accounted `$3050` for the fuel in one hour show. The number of Sukhoi planes is :

Options

A. 20
B. 30
C. 40
D. 50

Answer

To solve the problem, we need to set up a system of equations based on the information given. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( x \) = number of Sukhoi planes
- \( y \) = number of MiG-21 planes

### Step 2: Set Up the First Equation
According to the problem, the total number of aircraft is 90. Therefore, we can write our first equation as:
\[ x + y = 90 \quad \text{(1)} \]

### Step 3: Set Up the Second Equation
Next, we need to calculate the total fuel cost. The fuel consumption and costs are given as follows:
- A Sukhoi consumes 2 liters of fuel per hour at $10 per liter. Thus, the cost for one Sukhoi per hour is:
\[ 2 \text{ liters} \times 10 \text{ dollars/liter} = 20 \text{ dollars} \]
So, for \( x \) Sukhoi planes, the total cost is:
\[ 20x \quad \text{(2)} \]

- A MiG-21 consumes 3 liters of fuel per hour at $15 per liter. Thus, the cost for one MiG-21 per hour is:
\[ 3 \text{ liters} \times 15 \text{ dollars/liter} = 45 \text{ dollars} \]
So, for \( y \) MiG-21 planes, the total cost is:
\[ 45y \quad \text{(3)} \]

According to the problem, the total fuel cost for all aircraft is $3050. Therefore, we can write our second equation as:
\[ 20x + 45y = 3050 \quad \text{(4)} \]

### Step 4: Solve the System of Equations
Now we have a system of two equations:
1. \( x + y = 90 \) (Equation 1)
2. \( 20x + 45y = 3050 \) (Equation 4)

We can solve these equations simultaneously. First, we can express \( y \) from Equation (1):
\[ y = 90 - x \quad \text{(5)} \]

### Step 5: Substitute Equation (5) into Equation (4)
Substituting \( y \) from Equation (5) into Equation (4):
\[ 20x + 45(90 - x) = 3050 \]
Expanding this gives:
\[ 20x + 4050 - 45x = 3050 \]
Combining like terms:
\[ -25x + 4050 = 3050 \]
Now, isolate \( x \):
\[ -25x = 3050 - 4050 \]
\[ -25x = -1000 \]
Dividing both sides by -25:
\[ x = 40 \]

### Step 6: Find \( y \)
Now that we have \( x \), we can find \( y \) using Equation (5):
\[ y = 90 - x = 90 - 40 = 50 \]

### Conclusion
The number of Sukhoi planes is \( \boxed{40} \).

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