1) Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?



2) Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?



3) Carmen is trying to decide which jet ski rental plan to use. Plan A charges a one-time fee of $40 and $25 per hour. Plan B charges a one-time fee of $60 and $15 per hour. After how many hours will the plans cost the same?



4) Julie and Wendi purchased cell phones. Julie’s phone cost $50 and she pays $0.35 per minute. Wendi’s phone cost $70 and she pays $0.15 per minute. After how many minutes of use will Julie’s phone cost more than Wendi’s?



5) 78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?



6) 168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?



7) Christina spent $81.25 on books. Comic books cost $2.25 each and novels cost $7.00 each. If she bought 15 books, how many comic books did she buy?


8) Tina bought 8 pieces of clothing for a total of $164. Jeans cost $22 each and shirts cost $18 each. How many shirts did Tina buy?


9) Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?



10) Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?



What you need to do:

Please WRITE both equations for each problem, identify what your variables represent, and solve the system.

I don’t know what to do, so please help me understand by explaining how you got the answer.
I WANT TO LEARN FROM YOU! :)
- Will give BRAINLIEST if it gives me the option -

Respuesta :

Hey there!

Question no.5:

78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?

Solution:

Let the number of cars be "x" and the number of vans be "y".

According to question,

x + y = 10 5x + 12y = 78 -->(ii)

=> 5(x + y) = 10 × 5

=> 5x + 5y = 50 -->(i)

By Elimination method,

Equation (i) - (ii) we get,

(5x + 5y) - (5x + 12y) = 50 - 78

=> 5x + 5y - 5x - 12y = - 28

=> - 7y = - 28

=> 7y = 28

=> y = 28/7

=> y = 4

Putting the value of "y" in Equation (i)

5x + 5y = 50

=> 5x + 5 × 4 = 50

=> 5x + 20 = 50

=> 5x = 50 - 20

=> 5x = 30

=> x = 30/5

=> x = 6

Therefore,

The total number of cars went = 6

The total number of vans went = 4

====================================================

Question no.6:

168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?

Solution:

Let the number of buses be "x" and the number of vans be "y".

According to question,

x + y = 10 42x + 6y = 168 -->(ii)

=> 42(x + y) = 10 × 42

=> 42x + 42y = 420 -->(i)

By Elimination method,

Equation (i) - (ii)

(42x + 42y) - (42x + 6y) = 420 - 168

=> 42x + 42y - 42x - 6y = 252

=> 36y = 252

=> y = 252/36

=> y = 7

Putting the value of "y" in Equation (ii)

42x + 6y = 168

=> 42x + 6 × 7 = 168

=> 42x + 42 = 168

=> 42x = 168 - 42

=>42x = 126

=> x = 126/42

=> x = 3

Therefore,

Total number of buses went = 3

Total number of vans went = 7