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In a certain economy, C represents the total amount of

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Manager
Joined: 01 Sep 2012
Posts: 114
In a certain economy, C represents the total amount of  [#permalink]

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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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Joined: 02 Jul 2012
Posts: 1098
Location: India
Concentration: Strategy
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Re: In a certain economy, C represents the total amount of  [#permalink]

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14 Dec 2012, 21:00
3
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?

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

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

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

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

= 121

Manager
Joined: 01 Sep 2012
Posts: 114
Re: In a certain economy, C represents the total amount of  [#permalink]

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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

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...
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: In a certain economy, C represents the total amount of  [#permalink]

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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?

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

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

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

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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

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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Joined: 24 Apr 2012
Posts: 45
Re: In a certain economy, C represents the total amount of  [#permalink]

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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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Joined: 06 Sep 2013
Posts: 1545
Concentration: Finance
Re: In a certain economy, C represents the total amount of  [#permalink]

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

Then C=198 and Y=132

So Y increases by 121

D
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Posts: 9855
Location: Pune, India
Re: In a certain economy, C represents the total amount of  [#permalink]

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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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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
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: In a certain economy, C represents the total amount of  [#permalink]

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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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Posts: 8287
Re: In a certain economy, C represents the total amount of  [#permalink]

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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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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.

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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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