1) Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 3 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?
2) At the Dessert Island Pastry Cafe, there are 2 cakes for every 7 donuts and 11 brownies for every 3 cakes. What is the ratio of brownies to donuts?
Write your answer as a simplified fraction.
Its been 1800 secounds!!!!!
and I need to go in like 10 secounds ......
i need you to compose quicker!!!!
not to be rude
Let the amount of Alice's original money = A
Let the amount of Bob's original money = B
(A + n )* 3 = (B - n) → 3A + 3n = B - n → 3A - B = -4n (1)
(A - n) = 2 * ( B + n) → A - n = 2B + 2n → A - 2B = 3n (2)
Multiply the first equation by 3 and the second equation by 4 and add them together
9A - 3B = -12n
4A - 8B = 12n
13A - 11B = 0 add 11B to both sides
13A = 11B divide both sides by 13, B
A / B = 11 / 13
At the Dessert Island Pastry Cafe, there are 2 cakes for every 7 donuts and 11 brownies for every 3 cakes. What is the ratio of brownies to donuts?
2 cakes : 7 donuts → 6 cakes : 21 donuts
3 cakes : 11 brownies → 6 cakes : 22 brownies
22 brownies : 21 donuts