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# Mark has twice as many oranges as George. Tony has 10 less than twice

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Math Expert
Joined: 02 Sep 2009
Posts: 58347
Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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01 Nov 2018, 00:36
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:49) correct 23% (03:01) wrong based on 31 sessions

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Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?

A. 10
B. 15
C. 20
D. 25
E. 50

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Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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01 Nov 2018, 00:49
Bunuel wrote:
Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?

A. 10
B. 15
C. 20
D. 25
E. 50

We have been given a lot of information. Let us denote the # of oranges with Mark etc. by the first letter of the name. Also, the final ask is How many oranges did George have originally? or in our notation G=?

$$M = 2G$$
$$T = 2(G+M) -10$$
$$T/2 = G+15$$
$$T/2 = M+5$$

No we clearly have more equations than the number of unknowns, and the fastest way to solve would be to keep in mind what is being asked ( G=?)

$$M=2G$$
$$T = 2G+2M -10$$ Lets substitute from the first equation into this one to get rid of M.

$$T = 2G + 2(2G) -10$$
$$T = 6G -10$$

Second question : $$T = 2G + 30$$

$$2G + 30 = 6G - 10$$
$$4G = 40$$
$$G = 10$$

Hence option (A) is our choice.

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Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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01 Nov 2018, 05:03
Bunuel wrote:
Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?

A. 10
B. 15
C. 20
D. 25
E. 50

"Mark has twice as many oranges as George."
M = 2*G

"Tony has 10 less than twice the sum of George and Marks oranges."
T = 2*(G + M) - 10 = 2*(G + 2G) - 10 = 6G - 10

"If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally."
(6G - 10)/2 = G + 15 = 2G + 5

G = 10

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Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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03 Nov 2018, 01:23
my approach
M=2G
T=2(G+M)-10

M+5+G+15=2(G+M)-10
M+G+20=2G+2M-10
M+G=2G+2M-30
0=G+M-30
G+M=30

M=2G
3G=30
G=10
Re: Mark has twice as many oranges as George. Tony has 10 less than twice   [#permalink] 03 Nov 2018, 01:23
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