Respuesta :
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,
[tex]a_1x+b_1y+c_1=0[/tex]
[tex]a_2x+b_2y+c_2=0[/tex]
[tex]\frac{x}{b_1c_2-b_2c_2}=\frac{y}{a_2c_1-a_1c_2}=\frac{1}{a_1b_2-a_2b_1}[/tex]
[tex]{x}=\frac{b_1c_2-b_2c_2}{a_1b_2-a_2b_1}[/tex]
[tex]{y}=\frac{a_2c_1-a_1c_2}{a_1b_2-a_2b_1}[/tex]
Here [tex]a_1=33[/tex],[tex]b_1=20[/tex],[tex]c_1=-2025[/tex], [tex]a_2=30[/tex],[tex]b_2=11[/tex],[tex]c_2=-1827[/tex]
[tex]\therefore x=\frac{20.(-1827)-11.(-2025)}{33.11-30.20}[/tex] [tex]y=\frac{30.(-2025)-33.(-1827)}{33.11-30.20}[/tex]
[tex]\approx 40.41[/tex] [tex]\approx 1.94[/tex]
Therefore the cost of a crab meal and a vegetarian are $40.41 and $1.94 respectively.
