Question

One troop member So tickets for 33 crab meals and 20 vegetarian meals with a total receipt of $2025 another sold tickets for 30 for crab meals and 11 vegetarian meals and it's total of $1827 how much do the two type of tickets cost

Answer 1

Answer:

Therefore the cost of a crab meal and a vegetarian are $40.41 and $1.94 respectively.

Step-by-step explanation:

Given that,tickets for 33 crab meals and 20 vegetarian meal with total receipt of $2025. Another sold ticket for 30 crab meal and 11 vegetarian meals with total receipt of $1827.

Let the cost of a crab meal and a vegetarian meal be x and y respectively.

The cost of a crab meal is x

The cost of 33 crab meal is $33x

The cost of 30 crab meal is $30x

The cost of a vegetarian meal is y.

The cost of 20 vegetarian meal is $20y.

The cost of 11 vegetarian meal is $11y

According to problem,

33x+20y=2025

33x+20y-2025=0........(1)

        and

30x+11y=1827

30x+11y-1827=0 ..........(2)

Cross Multiplication Method,

$a_1x+b_1y+c_1=0$

$a_2x+b_2y+c_2=0$

$\frac{x}{b_1c_2-b_2c_2}=\frac{y}{a_2c_1-a_1c_2}=\frac{1}{a_1b_2-a_2b_1}$

${x}=\frac{b_1c_2-b_2c_2}{a_1b_2-a_2b_1}$

${y}=\frac{a_2c_1-a_1c_2}{a_1b_2-a_2b_1}$

Here $a_1=33$,$b_1=20$,$c_1=-2025$, $a_2=30$,$b_2=11$,$c_2=-1827$

$\therefore x=\frac{20.(-1827)-11.(-2025)}{33.11-30.20}$                   $y=\frac{30.(-2025)-33.(-1827)}{33.11-30.20}$

     $\approx 40.41$                                              $\approx 1.94$

Therefore the cost of a crab meal and a vegetarian are $40.41 and $1.94 respectively.