SOLUTION: Alvin had $250 more than Shufun. After both had spent 1/2 of what they had, the ratio of Alvin’s money to Shufun became 3:2. Alvin then gave Shufun money to make the new ratio 9:16

Algebra.Com
Question 1095254: Alvin had $250 more than Shufun. After both had spent 1/2 of what they had, the ratio of Alvin’s money to Shufun became 3:2. Alvin then gave Shufun money to make the new ratio 9:16.
(A) how much money did Alvin start with
(B) how much did Alvin give to Shufun
X/2 + (x+250)/2 = 3:2

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Alvin had $250 more than Shufun. After both had spent 1/2 of what they had, the ratio of Alvin’s money to Shufun became 3:2. Alvin then gave Shufun money to make the new ratio 9:16.
(A) how much money did Alvin start with
(B) how much did Alvin give to Shufun
X/2 + (x+250)/2 = 3:2
let original amount Alvin had, be A
Then original amount Shufun had = A - 250
After spending  of his money, Alvin had: 
After spending  of his money, Shufun had: 
We then get: 
				
				
3(A - 250) = 2A ------- Cross-multiplying				
3A - 750 = 2A
- 750 = 2A - 3A
- 750 = - A

Shufun's original amount: 750 - 250 = $500

Since Alvin had $750, originally, and spent , or $375, he then had $375 left
Since Shufun had $500, originally, and spent , or $250, he then had $250 left

Let the amount Alvin gave Shufun, be y. We get the following equation:				

9(250 + y) = 16(375 - y) ------- Cross-multiplying	
2,250 + 9y = 6,000 - 16y
9y + 16y = 6,000 - 2,250
25y = 3,750			
Amount given to Shufun by Alvin, or 

RELATED QUESTIONS

A sum of money was shared between Alvin, Zachary and Philip in the ratio 2:5:3... (answered by greenestamps)
A sum of money was shared between Alvin, Zachary and Philip in the ratio 2:5:3... (answered by AnlytcPhil)
Hi michael had 80% more money than alvin.vanessa had 40% less than alvin. Michael and... (answered by Theo)
The ratio of the amount of money Jim had to the amount of money Chris had was 7:10. After (answered by josgarithmetic)
Hi Mary and Gary had some stickers in the ratio of 5 to 3 respectively. After mary had... (answered by greenestamps)
Hi at first the ratio of bob and teds money was 5 to 2 . After each of them spent an... (answered by josgarithmetic,ikleyn,greenestamps)
Asher had $460 more money than Oscar at first. After Asher spent 3/4 of his money to buy... (answered by ikleyn,josgarithmetic)
Jack and Miya had some cards.In a game,Jack lost 1/10 of his card to Miya. After Jack... (answered by ankor@dixie-net.com)
The ratio of Jack’s allowance to John’s allowance was 1:3. After they each spent $68... (answered by greenestamps)