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# I need detailed explanation

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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?

Nov 3, 2021

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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

May 14, 2022