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](https://tex.z-dn.net/?f=a_1x%2Bb_1y%2Bc_1%3D0)
![a_2x+b_2y+c_2=0](https://tex.z-dn.net/?f=a_2x%2Bb_2y%2Bc_2%3D0)
![\frac{x}{b_1c_2-b_2c_2}=\frac{y}{a_2c_1-a_1c_2}=\frac{1}{a_1b_2-a_2b_1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bb_1c_2-b_2c_2%7D%3D%5Cfrac%7By%7D%7Ba_2c_1-a_1c_2%7D%3D%5Cfrac%7B1%7D%7Ba_1b_2-a_2b_1%7D)
![{x}=\frac{b_1c_2-b_2c_2}{a_1b_2-a_2b_1}](https://tex.z-dn.net/?f=%7Bx%7D%3D%5Cfrac%7Bb_1c_2-b_2c_2%7D%7Ba_1b_2-a_2b_1%7D)
![{y}=\frac{a_2c_1-a_1c_2}{a_1b_2-a_2b_1}](https://tex.z-dn.net/?f=%7By%7D%3D%5Cfrac%7Ba_2c_1-a_1c_2%7D%7Ba_1b_2-a_2b_1%7D)
Here
,
,
,
,
,![c_2=-1827](https://tex.z-dn.net/?f=c_2%3D-1827)
![y=\frac{30.(-2025)-33.(-1827)}{33.11-30.20}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B30.%28-2025%29-33.%28-1827%29%7D%7B33.11-30.20%7D)
![\approx 1.94](https://tex.z-dn.net/?f=%5Capprox%201.94)
Therefore the cost of a crab meal and a vegetarian are $40.41 and $1.94 respectively.