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The ratio of local and international calls made by Amy this week is 5

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The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post 08 Nov 2016, 00:24
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The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21

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The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post Updated on: 08 Nov 2016, 01:04
Bunuel wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21


IMO D
The ratio of local and international calls made by Amy this week is 5 to 2
let the current ratio be 5x/2x
the ratio changes to 5 to 3 after Amy makes three more international calls
5x/(2x+3)= 5/3
solving we get x=3
initial ratio 15:6 (5:2) final ratio 15:(6+3)= 15:9= 5:3
so total number of local calls=15

Originally posted by Vinayak Shenoy on 08 Nov 2016, 01:00.
Last edited by Vinayak Shenoy on 08 Nov 2016, 01:04, edited 1 time in total.
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Re: The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post 08 Nov 2016, 10:22
Bunuel wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21


Since the denominator changes from 2x to 3x

x = 3

So, 5x ( ie, Total Number o of Local calls ) is 15

Answer will be (D) 15

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Re: The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post 09 Nov 2016, 06:00
The ratio of local and international calls made by Amy this week is 5 to 2
let the local calls made by Amy this week = 5K
International calls made by Amy this week = 2K

Amy made 3 international calls, the ratio changes to 5:3 = 5k : 2K+3
solving we get K=3

The local calls made by Amy this week = 5K = 5*3 =15
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Re: The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post 09 Nov 2016, 10:02
Bunuel wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21


We are given that the ratio of local and international calls made by Amy this week is 5 to 2. Thus we can create the following ratio:

local calls : international calls = 5x : 2x

We are also given that the ratio changes to 5 to 3 after Amy makes three more international calls. Using this information, we can create the following equation:

5x/(2x + 3) = 5/3

Cross-multiplying gives us:

15x = 5(2x + 3)

15x = 10x + 15

5x = 15

x = 3

Since x = 3, the number of local calls made this week is 5(3) = 15.

Answer: D
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Re: The ratio of local and international calls made by Amy this week is 5  [#permalink]

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New post 27 Feb 2018, 15:31
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Bunuel wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21


Let L = number of local calls made this week
Let N = number of international calls made this week

The ratio of local and international calls made by Amy this week is 5 to 2
So, L/N = 5/2
Cross multiply to get: 2L = 5N

The ratio changes to 5 to 3 after Amy makes three more international calls
So, now N+3 = number of international calls made this week
And L still equals number of local calls made this week
We can write: L/(N + 3) = 5/3
Cross multiply to get: 3L = 5(N + 3)
Expand to get: 3L = 5N + 15

We know have the following system of equations
3L = 5N + 15
2L = 5N

SUBTRACT the bottom equation from the top equation to get: L = 15

Answer: D

Cheers,
Brent
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Re: The ratio of local and international calls made by Amy this week is 5 &nbs [#permalink] 27 Feb 2018, 15:31
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