Use the system of equation to solve the following problem. Define the variables

Question

Use the system of equation to solve the following problem. Define the variables in your equation. Don't guess and check
1. Castle and Gabriella are selling for a school fundraiser. Customers can buy Apple pies and lemon meringue pies . Castle sold 7 Apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 Apple pies and 5 lemon meringue pies for a total of $94. What is the cost of each of one Apple pie and one lemon meringue pie. 2. The local amusement park is a popular field trip destination. This year the senior class at high school A and the senior class at High school B both planned trips there . The senior class at high school a rented and filled 16 vans and 8 buses with with 752 students .high school N rented and filled 5 vans and 5 buses with 380 students . Each can and each bus carried the same amount of students . How many students can a van carry? How many students can a bus carry ?
Show all work for both questions please! Use the system of equation to solve the following problem. Define the variables in your equation. Don't guess and check
1. Castle and Gabriella are selling for a school fundraiser. Customers can buy Apple pies and lemon meringue pies . Castle sold 7 Apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 Apple pies and 5 lemon meringue pies for a total of $94. What is the cost of each of one Apple pie and one lemon meringue pie. 2. The local amusement park is a popular field trip destination. This year the senior class at high school A and the senior class at High school B both planned trips there . The senior class at high school a rented and filled 16 vans and 8 buses with with 752 students .high school N rented and filled 5 vans and 5 buses with 380 students . Each can and each bus carried the same amount of students . How many students can a van carry? How many students can a bus carry ?
Show all work for both questions please!
1. Castle and Gabriella are selling for a school fundraiser. Customers can buy Apple pies and lemon meringue pies . Castle sold 7 Apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 Apple pies and 5 lemon meringue pies for a total of $94. What is the cost of each of one Apple pie and one lemon meringue pie. 2. The local amusement park is a popular field trip destination. This year the senior class at high school A and the senior class at High school B both planned trips there . The senior class at high school a rented and filled 16 vans and 8 buses with with 752 students .high school N rented and filled 5 vans and 5 buses with 380 students . Each can and each bus carried the same amount of students . How many students can a van carry? How many students can a bus carry ?
Show all work for both questions please!

Explanation / Answer

1. Solution: Let the cost of one Apple pie be x and one lemon meringue pie be y.

According to the question,

7x + 4y = 80 ....(i)

And

6x + 5y = 94 ....(ii)

Multiply equation (i) by 5, to get

35x + 20 y = 400 ...(iii)

Multiply equation (ii) by 4, to get

24x + 20 y = 376 ....(iv)

Subtracting equation (ii) from (i) , to get

11 x = 400 - 376

or 11 x = 24   

or x = 24/11

or x = 2.18

Now substitute the value of x in the equation (i), to get

7 (24/11) + 4y = 80

or 4y = 80 - 168/11

or 4y = (880 - 168 ) /11

or     4y = (712 ) /11

or y = 712 /44

or y = 178 /11

or     y = 16.18

Hence the cost of one Apple pie is 2.18 and one lemon meringue pie is 16.18. Ans

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2. Solution: Let one van carries x students and one bus carries y students.

According to the question,

16x + 8y = 752 ...(...16 vans and 8 buses with with 752 students)

or 2x + y = 94 ....(i)

5x+ 5y = 380 ...(...5 vans and 5 buses with 380 students)

or x + y = 76 ....(ii).

Subtract equation (ii) from the equation (i), to get

x = 94-76

x = 18.

Now substitute this value of x in the equation (ii), to get

18 + y = 76

or y = 58.

Hence a van carries 18 students and a bus carries 58 students. Ans

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