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