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In a certain economy, C represents the total amount of

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In a certain economy, C represents the total amount of  [#permalink]

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New post 14 Dec 2012, 13:27
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In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 14 Dec 2012, 21:00
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roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?


A.11
B.22
C.99
D.121
E.171


I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?


\(C_{old} = 90 + \frac{9Y_{old}}{11}\)

\(Y_{old} = \frac{(C_{old} - 90)*11}{9}\)

\(Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}\)

\(Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}\)

= 121

Answer is D
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 15 Dec 2012, 03:07
MacFauz wrote:
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?


A.11
B.22
C.99
D.121
E.171


I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?


\(C_{old} = 90 + \frac{9Y_{old}}{11}\)

\(Y_{old} = \frac{(C_{old} - 90)*11}{9}\)

\(Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}\)

\(Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}\)

= 121

Answer is D


Ok so your thinking process was - i need to find an increase hence subtract Yold and Ynew.
I did isolated Y and then instead of C i put C+99 but wasnt aware that i should treat them as Old and New.
interesting...
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 15 Dec 2012, 05:54
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?


\(C=90+\frac{9Y}{11}\) --> \(Y=\frac{11C}{9}-9*11\).

\(Y_1=\frac{11C}{9}-9*11\);
\(Y_2=\frac{11(C+99)}{9}-9*11=\frac{11C}{9}+11*11-9*11=(\frac{11C}{9}-9*11)+121\).

Answer: D
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 15 Dec 2012, 07:14
MacFauz wrote:
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?


A.11
B.22
C.99
D.121
E.171


I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?


\(C_{old} = 90 + \frac{9Y_{old}}{11}\)

\(Y_{old} = \frac{(C_{old} - 90)*11}{9}\)

\(Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}\)

\(Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}\)

= 121

Answer is D



I like your approach step by step, is fine. :)

But also if we do :C = 90 + 9y/11 ------> adding 99 we have 11 (C - 90 +99)/9= y -------> 11C + 99/9 = Y clearly the only value that fits is 11 * 2 + 99/9 = y. \(That is, 121\)
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 16 Dec 2012, 04:18
Ans:
C = 90 + 9y/11 , adding 99 we have 11 (C - 90 +99)/9= y , (11C + 99)/9 = Y , so the increase is Y-y=121 the answer is (D).
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 30 Jan 2014, 07:41
Just assume y=11 and C=99

Then C=198 and Y=132

So Y increases by 121

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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 30 Jan 2014, 21:20
1
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?


Given \(C = 90 + \frac{9Y}{11}\)
Note that C changes whenever Y changes. So if C increases by 99, it's because Y increased from Y1 to Y2.

\(\frac{9}{11}(Y2 - Y1) = 99\)
\(Y2 - Y1 = 121\)
Y increased by 121 which led to an increase of 99 in C.
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In a certain economy, C represents the total amount of consumption in  [#permalink]

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New post 09 Mar 2016, 11:17
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation \(C= 90+\frac{9}{11}y\) . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A) 11

B) 22

C) 99

D) 121

E) 171
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 09 Mar 2016, 11:21
ninayeyen wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation \(C= 90+\frac{9}{11}y\) . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A) 11

B) 22

C) 99

D) 121

E) 171


Merging topics. Please refer to the discussion above.
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 10 Mar 2016, 07:48
ninayeyen wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation \(C= 90+\frac{9}{11}y\) . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A) 11

B) 22

C) 99

D) 121

E) 171


hi,
lets see the equation-
\(C= 90+\frac{9}{11}y\) ..

here 90 is a constant term, so ANY increase / decrease in C will be COMPENSATED by y..
so an increase of 99 will be taken care by y..

\(99= \frac{9}{11}y\) or y=121..
D
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Re: In a certain economy, C represents the total amount of  [#permalink]

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New post 24 Nov 2019, 18:49
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?



Let x be the increase in the total national income. We can create the equation:

C + 99 = 90 + 9(Y + x)/11

However, since C = 90 + 9Y/11, we have:

90 + 9Y/11 + 99 = 90 + 9(Y + x)/11

9Y/11 + 99 = 9Y/11 + 9x/11

99 = 9x/11

11 = x/11

121 = x

Alternate Solution:

Let’s begin by expressing Y in terms of C:

C = 90 + (9/11)Y

11C = 990 + 9Y

9Y = 11C - 990

Y = (11/9)C - 110

Now, suppose C increases by 99, i.e., C becomes C + 99. Then,

(11/9)(C + 99) - 110 = (11/9)C + 121 - 110 = (11/9)C - 110 + 121

Since (11/9)C - 110 = Y; we have:

(11/9)C - 110 + 121 = Y + 121

Thus, we see that when C increases to C + 99, Y increases to Y + 121.

Answer: D
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Re: In a certain economy, C represents the total amount of   [#permalink] 24 Nov 2019, 18:49
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