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# John has \$42. He purchased fifty mangoes and thirty oranges with the

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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14 Apr 2019, 21:46
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Difficulty:

35% (medium)

Question Stats:

79% (01:58) correct 21% (02:20) wrong based on 19 sessions

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John has \$42. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

(A) 0.4
(B) 0.45
(C) 0.5
(D) 0.55
(E) 0.6

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Joined: 17 May 2018
Posts: 140
Location: India
Re: John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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14 Apr 2019, 22:02
I solved with simultaneous end
50m+30o= 42
44m+39o= 42
Is there a faster method to do this?

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Re: John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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15 Apr 2019, 01:31
Bunuel wrote:
John has \$42. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

(A) 0.4
(B) 0.45
(C) 0.5
(D) 0.55
(E) 0.6

given
50m+30O=42
and
6m=9O
2m=3O
O= 2/3M
so 50m+30*2M/3=42
solve for M = 42/70 ;
IMO E 0.6
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Re: John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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15 Apr 2019, 02:56
Bunuel wrote:
John has \$42. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

(A) 0.4
(B) 0.45
(C) 0.5
(D) 0.55
(E) 0.6

Given,

50 M + 30 Or = 42

and,

6 M = 9 or

2 M = 3 Or

Thus we can manipulate the 1st equation.

50 M + 30 Or = 42

50 M + 20 M = 42

70 M = 42

M = 42/70 = 6/10 = 3/5 = 0.6.

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Re: John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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15 Apr 2019, 03:15
50M+30O =42
5M+3O=4.2........(I)

Now
6M=9O
2M=3O
Substitute in I
7M = 4.2
M = 0.6
E

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Re: John has \$42. He purchased fifty mangoes and thirty oranges with the  [#permalink]

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16 Apr 2019, 17:53
Bunuel wrote:
John has \$42. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

(A) 0.4
(B) 0.45
(C) 0.5
(D) 0.55
(E) 0.6

Letting m = the price of one mango and r = the price of one orange, we can create the equations:

50m + 30r = 42

and

6m = 9r

2m = 3r

2m - 3r = 0

Multiplying 2m - 3r = 0 by 10 and adding this to the first equation, we have:

70m = 42

m = 42/70 = 6/10 = 0.6

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Re: John has \$42. He purchased fifty mangoes and thirty oranges with the   [#permalink] 16 Apr 2019, 17:53
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