Help with 3 challenging ratio problems? (SHSAT Prep)?
*A clown had 42 red balloons and 66 blue balloons. After he gave an equal number of red balloons and blue balloons away, the ratio of the number of red balloon to the number of blue balloons was 4:7. How many balloons did he give away altogether?
*George and Alfred had the same number of greeting cards. After George used 6 greeting cards and Alfred used 30 greeting cards, the ratio of the number of George’s greeting cards to the number of Alfred’s greeting cards was 7:5. How many greeting cards did they have left?
*Three boxes, A, B, and C, had 260 ping pong balls. Lisa added some ping pong balls into box A and the number of ping pong balls in box A tripled. She took out half of the ping pong balls in box B and added 40 ping pong balls into box C. The ratio of the number of ping pong balls in box A, B, and C became 6:4:5. Find the original ratio of the number of ping pong balls in boxes A, B, and C.
Please show your work and thank you for answering 
1)
Let x be the amount of red and blue balloons given away. Then, the new number of red balloons is 42 – x and the new number of blue balloons is 66 – x.
Since the ratio is 4:7, we have:
(42 – x)/(66 – x) = 4/7.
If you solve this for x, you get x = 10 and so 10 + 10 = 20 balloons are given away.
2)
Let x be the amount of initial greeting cards that both George and Alfred have.
Since George used 6 of them, he now has x – 6; and since Alfred used 30 of them, he now has x – 30.
This gives:
(x – 6)/(x – 30) = 7/5.
This has a solution of x = 90 and so George has 84 left and Alfred has 60 left.
3)
Since Lisa tripled the amount of ping-pong balls in box A, box A has 260*3 = 780 ping-pong balls. Using the Ratio 6:4:5 given, box B has 4/6 * 780 = 320 ping-pong balls and box C has 5/6 * 780 = 650 ping-pong balls.
Then, box C originally had 650 – 40 = 610 ping-pong balls and box B original had 2*320 = 640 ping-pong balls.
Thus, the original ratio is 780:640:610 = 78:64:61.
I hope this helps!
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