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

Question

Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Mark`s 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

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

Gladiator59 · Answer

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.

Best,
Gladi

KarishmaB · Answer

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

"Tony has 10 less than twice the sum of George and Mark`s 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

Answer (A)

Gegeyan · Answer

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

Bytruelyyours · Answer

M=2G
T=2(G+M)-10
G+15=0.5T 
M+5=0.5T 
(SAME EQUATION SO EQUATE ) 
G+15=M+5 
G+15=2G+5
G-2G=5-15 
G=10

ThatDudeKnows · Answer

Let's just plug in the answers. I like trying B and D.
B: George has 15. Mark has 30. Tony has 2*45 - 10 = 80. 
Tony gives 15 to George and 5 to Mark. George now has 30. Mark now has 35. 
Nope. We need George and Mark to be closer together. We also need Tony to be lower.
Answer choice A is the only one that does either of those things.

Answer choice A.

If you need to confirm A,
George has 10. Mark has 20. Tony has 2*30 - 10 = 50.
Tony gives 15 to George and 5 to Mark. George now has 25. Mark now has 25.
Yep.

luisdicampo · Answer

Deconstructing the Question  
Let George have  G , Mark have  M , Tony have  T  initially.
Given:
 M=2G 
 T=2(G+M)-10 
After Tony gives 15 to George and 5 to Mark:
 G+15=\frac{T}{2} 
 M+5=\frac{T}{2}

Key idea: both equal  \frac{T}{2} , so set them equal to connect G and M.

Step-by-step

G+15=M+5 
 G+10=M

Using  M=2G :
 G+10=2G 
 G=10

Check:
 M=20 
 T=2(10+20)-10=50 
Then  G+15=25  and  M+5=25 , which is half of 50.

Answer: 10

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

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

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