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


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

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

Answer: D
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Re: In a certain economy, C represents the total amount of [#permalink]
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]
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]
Just assume y=11 and C=99

Then C=198 and Y=132

So Y increases by 121

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


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



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