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jar contains pink and green marbles in the ratio 3 : 4. When John replaces 5 of the green marbles with 8 pink marbles, the ratio becomes 29 : 23. The ratio of the total number of marbles in the jar after replacement to the total number of marbles in the jar originally is : .

User Jhoff
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2 votes

Answer:

52:49

Explanation:

pink:green

The ratio of pink to green marbles is

3k:4k

He removes 5 green marbles and adds 8 pink marbles.

Now the ratio of pink to green marbles is

(3k + 8):(4k - 5)

This rario is equal to 29:23.

(3k + 8)/(4k - 5) = 29/23

29(4k - 5) = 23(3k + 8)

116k - 145 = 69k + 184

47k = 329

k = 7

Original amounts:

3 * k = 3 * 7 = 21 pink

4 * k = 4 * 7 = 28 green

Original total = 21 + 28 = 49

Amounts after replacement:

3k + 8 = 3(7) + 8 = 29 pink

4k - 5 = 4(7) - 5 = 23 green

Total after replacement = 23 + 29 = 52

Answer: The ratio of the total number of marbles in the jar after replacement to the total number of marbles in the jar originally is 52:49.

User Formica
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