Question 1206829
i get 30 toys.


here's my thinking.


you start with:


2/7 * x = 4 dolls and 8 books.
5/7 * x = 6 dolls and 12 books and 10 toys.


6 dolls is 1.5 * 4 dolls.
12 books is 1.5 * 8 books.


since 4 dolls and 8 books = 2/7 * x, then 1.5 * (4 dolls and 8 books) = 1.5 * 2/7 * x.


1.5 * 2/7 * x = 3/7 * x


since 3/7 * x = 6 dolls and 12 books, then 2/7 * x must be equal to 10 toys.


6/7 * x = 3 * 2/7 * x, therefore you must be able to buy 30 toys with 6/7 * x.


algebraically it would look like this.


let d = number of dolls and b = number of books and let t = number of toys.


you have 2 equations that need to be solved simultaneously.


they are:


4d + 8b = 2/7 * x
6d + 12b + 10t = 5/7 * x


multiply both sides of the first equation by 1.5 and leave the second equation as is to get:


6d + 12b = 3/7 * x
6d + 12b + 10t = 5/7 * x


subtract the first equation from the second to get:


10t = 2/7 * x.


6/7 * x = 3 * 2/7 * x, therefore multiply both sides of that equation by 3 to get:


30t = 6/7 * x.


that's your answer.