Brandon and Bobby had 80 marbles in total. Brandon had 36 marbles less than Bobby at first. After Brandon and Bobby played a game with Natalie, Brandon had ¹₁₀ as many marbles as Bobby. If Brandon lost as many marbles as Bobby to Natalie, find the number of marbles that Bobby lost to Natalie.

	Brandon	Bobby	Difference
Before	1 u	1 u + 36	36
Change	- ?	- ?
After	1 p	10 p	9 p

Total number of marbles at first
= 1 u + 1 u + 36 
= 2 u + 36

2 u + 36 = 80
2 u = 80 - 36
2 u = 44

1 u = 44 ÷ 2 = 22

Since Brandon lost the same number of marbles as Bobby, the difference in the number of marbles between Brandon and Bobby at first and in the end remains the same.

Difference in the number of marbles in the end
= 10 p - 1 p
= 9 p

9 p = 36

1 p = 36 ÷ 9 = 4

Number of marbles that Brandon lost to Natalie
= 1 u - 1 p
= 22 - 1 x 4
= 22 - 4
= 18

Since Bobby lost the same number of marbles as Brandon, the number of marbles that each lost to Natalie is the same.

Number of marbles that Bobby lost = 18

Answer(s): 18