I have a problem I've been trying to help with my seventh grade daughter Nicole this afternoon: Two sisters, Mary and Julia, shared $72. When their mother gave them another $10 each, Julia had 16% less month than Mary. What is the ratio of the amount of Mary's money to the amount of Julia's money at first?
I don't think that Nicole has had two variables yet. I did it this way:
(x+10) + (y+10) = 92
(y+10) = .84(x+10)
Then, substituting .84(x+10) for (x+10) in the first equation I got
(x+10) + ,84(x+10) = 92 and then,
1.84x + 18.4 - 92 or 1.84x = 73.6
Dividing both sides by 1.84 I got x = 40
So Mary has $40 and Julia $32 before the extra $10 each, or $50 and $42 with the $10 extra. $42 is 16% less than $50
So the relationship of the original money $40 and $32 is 40/32 or 1.25:1. Right?
But Nicole with flip out if I even suggest this method. There must be some other more simple method that is escaping me. Any thoughts?
Rick
I don't think that Nicole has had two variables yet. I did it this way:
(x+10) + (y+10) = 92
(y+10) = .84(x+10)
Then, substituting .84(x+10) for (x+10) in the first equation I got
(x+10) + ,84(x+10) = 92 and then,
1.84x + 18.4 - 92 or 1.84x = 73.6
Dividing both sides by 1.84 I got x = 40
So Mary has $40 and Julia $32 before the extra $10 each, or $50 and $42 with the $10 extra. $42 is 16% less than $50
So the relationship of the original money $40 and $32 is 40/32 or 1.25:1. Right?
But Nicole with flip out if I even suggest this method. There must be some other more simple method that is escaping me. Any thoughts?
Rick