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.
Accepted Solution
A:
There are 21 books Jason's have and 24 books Nathan's have.GivenSix 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. Let the number of collection of books Jason's be x.And the number of collection of books Nathan's be y.Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.[tex]\rm 6x+\dfrac{1}{3} y=134\\\\\dfrac{18x+y}{3} =134\\\\ 18x+y = 134\times 3\\\\18x+y=402[/tex]One-third of Jason's collection and Nathan's entire collection add up to 31 books.[tex]\rm \dfrac{1}{3}x+y=31\\\\\dfrac{x+3y}{3} =31\\\\x+3y=31\times 3\\\\x+3y=93[/tex]On solving both the equations;From equation 1;[tex]\rm 18x+y=402\\\\y = 402-18x[/tex]Substitute the value of y in equation 2[tex]\rm x+3y=93\\\\x+ 3(402-18x)=93\\\\x+1206 -54x=93\\\\-53x = 93-1206\\\\-53x =-1113\\\\x = \dfrac{-1113}{-53}\\\\x=21[/tex]Substitute the value of x in equation 2[tex]\rm x+3y=93\\\\21+3y=93\\\\3y=93-21\\\\ 3y =72\\\\ y = \dfrac{72}{3} \\\\ y=24[/tex]Hence, there are 21 books Jason's have and 24 books Nathan's have.To know more about Equations click the link given below.