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

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Joined: 02 Sep 2009
Posts: 58313
The ratio of local and international calls made by Amy this week is 5  [#permalink]

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08 Nov 2016, 01:24
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:23) correct 23% (01:58) wrong based on 118 sessions

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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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Updated on: 08 Nov 2016, 02:04
1
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, 02:00.
Last edited by Vinayak Shenoy on 08 Nov 2016, 02:04, 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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08 Nov 2016, 11:22
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

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

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09 Nov 2016, 07:00
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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09 Nov 2016, 11:02
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.

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

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27 Feb 2018, 16:31
1
Top Contributor
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

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

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03 Sep 2019, 11:19
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Re: The ratio of local and international calls made by Amy this week is 5   [#permalink] 03 Sep 2019, 11:19
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