Ethan and Daniel have some marbles. If Ethan gives Daniel 16 marbles, both of them will have an equal number of marbles. If Daniel gives Ethan 9 marbles, the ratio of the number of marbles Ethan has to the number of marbles Daniel has will be 6:1. How many marbles do the two boys have altogether?
Let
No of marbles with Ethan = x
No of marbles Daniel has = y
If Ethan gives 16 marbles to David
both of them will have equal numner
∴ x - 16 = y + 16
x = y + 16 + 16
x = y + 32 ---- (1)
If Daniel gives 9 marbles to Ethan
x + 9 : y - 9
6 : 1
Total marbles = x + y (7 parts / units)
1 unit/part = (x + y)/7
(x + y)/7 * 6 = x + 9 (x + y)/7 * 1 = y - 9
---- (2)
Sub eqn (1) in (2)
(y + 32 + y)/7 * 6 = y + 32 + 9
(6(2y + 32))/7 = y + 41
12y + 192 = 7(y + 41)
12y + 192 = 7y + 287
12y - 7y = 287 - 192
5y = 95
y = 95/5 = 19
Sub y = 19 in eqn (1)
x = 19 + 32 = 51
Total marbles = x + y
= 51 + 19
= 70
