SOLUTION: the ratio of the number of Grace's Lego bricks to the number of Bobby's Lego bricks was 5:2. the ratio became 9:19 when Grace gave Bobby 220 bricks. a)how many lego bricks had B

Question 145062: the ratio of the number of Grace's Lego bricks to the number of Bobby's Lego bricks was 5:2. the ratio became 9:19 when Grace gave Bobby 220 bricks.
a)how many lego bricks had Bobby at first?
b)what fraction of Bobby's lego bricks was from Grace? (give answer in simplest form)

*pls try not to use algebra
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Well, we have to use a variable "x" here to represent the unknown. And what is that unknown, the number of lego bricks right? So remember "x" = no. of lego bricks.
1st condition,
Meaning for every 5 lego brick Grace has, Bobby has 2 lego brick right?
2nd condition,
We only satisfy this condition if Grace gave Bobby 220 bricks. Therefore our eqn will revolve on this condition.
Since the # of bricks is , Grace total will be and Bobby's total will be . Putting this into equation, the 2nd condition with the new total no. of bricks for both in solving question (a):
---------- 3rd condition
re arranging,

. This will be the original number of lego bricks that Bobby has.
In doubt? Go back condition 2, and substitute "x"

...note, factor out or divide both 396 & 836 by 44

The new # of bricks bobby has is 836, minus 220 given equals 616, got it?
For question (b), # of bricks given/ total # of bricks
= (divide both 220 & 836 by 4)
=. This is how much fraction Bobby's lego bricks that came from Grace.
Or 26.32% of Bobby's # of bricks came from Grace.
(55/2090(100%) = 26.32%

Thank you,
Jojo

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