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Question

Can anyone help me with this question? Thnks a lot.

Ricky had 260 more red marbles than blue marbles at first. After selling 1/7 of the blue marbles and 5/9 of the red marbles, he had an equal number of blue marbles and red marbles left. He then bought another 30 blue marbles. What was the ratio of the number of red marbles to the number of blue marbles Ricky had in the end? Express your answer in its simplest form.

Answer

Ricky had 260 more red marbles than blue marbles at first. After selling 1/7 of the blue marbles and 5/9 of the red marbles, he had an equal number of blue marbles and red marbles left. He then bought another 30 blue marbles. What was the ratio of the number of red marbles to the number of blue marbles Ricky had in the end? Express your answer in its simplest form.

Equation 1: 4 Red  – 6 blue = 0

Equation 2: 9 red – 7 blue = 260

Equation 3 [Equation 1 * 9]: 36 Red – 54 Blue = 0

Equation 4 [Equation 2 * 4]: 36 Red – 28 Blue = 1040

[Eq 4 – Eq 3]: 26 blue = 1040

blue = 40

40 * 6 = 240 [Remainder blue]

240 + 30 = 270 (Blue marbles in the end)

 

Red Leftover = 240 

Ratio 240: 279 = 8:9

 

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B —— 6/7 = 12/14

R —— 4/9 = 12/27

B -> sold 2u, left 12u, at first 14u

R -> sold 15u, left 12u, at first 27u

27u – 14u = 13u

13u -> 260

1u -> 260 ÷ 13 = 20

12u -> 12 x 20 = 240 (B and R left)

240 + 30 = 270 (B in the end)

R in the end = 240

R : B = 240 : 270 = 8 : 9 (Ans)

 

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