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(13200)   (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)  (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.
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