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 .

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.

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JeanaShupp JeanaShupp · Answer 2 · 2019-06-26T05:41:51+02:00

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

Step-by-step 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

[tex]6x+\dfrac{1}{3}y=134..........................(1)\\\\\dfrac{1}{3}x+y=31.....................................(2)[/tex]

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

[tex]54x+3y=1206..................................(3)\\\\x+3y=93.............................................(4)[/tex]

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

[tex]53x=1113[/tex]

Divide 53 on both sides, we get

[tex]x=21[/tex]

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

[tex]\dfrac{1}{3}(21)+y=31\\\\\Rightarrow\ 7+y=31\\\\\Righarrow\ y=24[/tex]

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