Question

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books. One-third of Jason's collection and Nathan's entire collection add up to 31 books. The number of books in Jason's collection is , and the number of books in Nathan's collection is .

Answer 1

Jason is x and Nathan is y.
1st equation: 6x + y/3 = 134
Times 3.
(6x + y/3 = 134)3 = (18x + y = 402)
2nd equation: x/3 + y = 31
→ Change signs. (- x/3 - y = -31)
Add both equations (18x+y=402) + (-x/3-y=-31) →
53x/3=371
Multiply both sides by 3 → 53x=1113
Divide both sides by 53→ x=21
21/3+y=31 → y=24
Answer: Jason= 21 books and Nathan= 24 books.

Answer 2

Answer: The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .

Explanation:

Let x represent the number of books Jason has and y represents the number of books Nathan has .

Then , According to the question , we have

`6x+(1)/(3)y=134..........................(1)\\\\(1)/(3)x+y=31.....................................(2)`

Multiply 9 in equation (1) and and 3 in equation (2), we get

`54x+3y=1206..................................(3)\\\\x+3y=93.............................................(4)`

Subtract equation (4) from equation (3), we get

`53x=1113`

Divide 53 on both sides, we get

`x=21`

Put the value of x in (2), we get

`(1)/(3)(21)+y=31\\\\\Rightarrow\ 7+y=31\\\\\Righarrow\ y=24`

Hence, The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .