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

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

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`

`(x)/(b_1c_2-b_2c_2)=(y)/(a_2c_1-a_1c_2)=(1)/(a_1b_2-a_2b_1)`

`{x}=(b_1c_2-b_2c_2)/(a_1b_2-a_2b_1)`

`{y}=(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=(20.(-1827)-11.(-2025))/(33.11-30.20)`
`y=(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.