SOLUTION: Hi Janet spent 2/7 of her money on 4 dolls and 8 books. She spent the remaining money on 6 dolls 10 toys and 12 books. How many toys could she buy with 6/7 of her money.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi Janet spent 2/7 of her money on 4 dolls and 8 books. She spent the remaining money on 6 dolls 10 toys and 12 books. How many toys could she buy with 6/7 of her money.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1206829: Hi
Janet spent 2/7 of her money on 4 dolls and 8 books. She spent the remaining money on 6 dolls 10 toys and 12 books. How many toys could she buy with 6/7 of her money.

Found 2 solutions by greenestamps, Theo:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Her first purchase of 4 dolls and 8 books cost her 2/7 of her money.

In her second purchase, she bought 6 dolls and 12 books. 6 dolls is 3/2 of 4 dolls, and 12 books is 3/2 of 8 books, so what she spent on dolls and books in the second purchase was 3/2 of what she spent on them in her first purchase.

3/2 of 2/7 is 3/7, so she spent 3/7 of her money on dolls and books in the second purchase.

Together in her two purchases she spent 2/7 + 3/7 = 5/7 of her money on dolls and books. Since she spent all her money, she spent 2/7 of her money on the 10 toys.

6/7 of her money is 3 times as much as 2/7 of her money. If she can buy 10 toys with 2/7 of her money, then she can buy 3*10 = 30 toys with 6/7 of her money.

ANSWER: 30


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.