Question

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 -

Answer 1

Hey there!

Question no.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?

Solution:

Let the number of cows be "x" and the number of chickens be "y".

According to question,

x + y = 25 4x + 2y = 72 -->(ii)

=> 4(x + y) = 25 × 4

=> 4x + 4y = 100 -->(i)

By Elimination method,

Equation (i) - (ii)

(4x + 4y) - (4x + 2y) = 100 - 72

=> 4x + 4y - 4x - 2y = 28

=> 2y = 28

=> y = 28/2

=> y = 14

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

4x + 2y = 72

=> 4x + 2 × 14 = 72

=> 4x + 28 = 72

=> 4x = 72 - 28

=> 4x = 44

=> x = 44/4

=> x = 11

Therefore,

Total number of cows = 11

Total number of chickens = 14

Note: In the second equation of this question I've taken 4 and 2.

The reason behind it is simple. Since, I've assumed the number of cows is "x" and a cow has four legs that why infront of "x" I've put 4.

And a chicken has 2 legs and I've assumed it as "y" therefore infront of "y" I've put 2.

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

Question no.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?

Solution:

Let the number of cows be "x" and the number of chickens be "y".

According to question,

x + y = 28 4x + 2y = 96 -->(ii)

=> 4(x + y) = 28 × 4

=> 4x + 4y = 112 -->(i)

By Elimination method,

Equation (i) - (ii)

(4x + 4y) - (4x + 2y) = 112 - 96

=> 4x + 4y - 4x - 2y = 16

=> 2y = 16

=> y = 16/2

=> y = 8

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

4x + 2y = 96

=> 4x + 2 × 8 = 96

=> 4x + 16 = 96

=> 4x = 96 - 16

=> 4x = 80

=> x = 80/4

=> x = 20

Therefore,

Total number of cows = 20

Total number of chickens = 8

Note: In the second equation of this question I've taken 4 and 2.

The reason behind it is simple. Since, I've assumed the number of cows is "x" and a cow has four legs that why infront of "x" I've put 4.

And a chicken has 2 legs and I've assumed it as "y" therefore infront of "y" I've put 2.

Hope it helps