Pierre had ³₄ as many marbles as Howard. Howard had ⁴₇ as many marbles as Marion. After Pierre and Marion gave 26 marbles to Howard, Howard had thrice as many marbles as Pierre. Marion then had the same number of marbles as Howard.

1. What was the ratio of the number of marbles Marion had to the number of marbles Pierre had in the beginning? Answer in simplest form.
2. How many marbles did Howard have in the end?

Pierre	Howard	Marion
3	4
	4	7
3	4	7

(a)
The number of marbles that Howard is repeated.  

Ratio of the number of marbles that Marion had to the number of marbles that Pierre had in the beginning = 7 : 3

	Pierre	Howard	Marion	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 26	+ 52	- 26
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of marbles at first and in the end remains unchanged. Make the total number of marbles the same. LCM of 14 and 7 is 14.

Number of marbles that Howard received from Pierre and Marion
= 2 x 26
= 52

Number of marbles that Howard received from Pierre and Marion
= 2 x 1 u
= 2 u

2 u = 26

1 u = 26 ÷ 2 = 13

Number of marbles that Ashley had in the end
= 6 u
= 6 x 13
= 78