On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
A. 30
B. 60
C. 75
D. 90
E. 105
OA D
Source: Princeton Review
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of
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We are given the ratio of horses to cows is 7 to 3, or 7x to 3x. We can create the following equation:BTGmoderatorDC wrote: ↑Fri Feb 24, 2023 8:50 pmOn a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
A. 30
B. 60
C. 75
D. 90
E. 105
OA D
Source: Princeton Review
(7x  15)/(3x + 15) = 13/7
7(7x  15) = 13(3x + 15)
49x  105 = 39x + 195
10x = 300
x = 30
Thus, there are 7(30) = 210 horses and 3(30) = 90 cows in the farm before the transaction. After the transaction, there are 210  15 = 195 horses and 90 + 15 = 105 cows. So, there are 195  105 = 90 more horses than cows after the transaction.
Answer: D
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We can also solve this using TWO VARIABLESBTGmoderatorDC wrote: ↑Fri Feb 24, 2023 8:50 pmOn a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
A. 30
B. 60
C. 75
D. 90
E. 105
OA D
Source: Princeton Review
Let H = present number of horses
Let C = present number of cows
ratio of horses to cows is 7:3
So, H/C = 7/3
Cross multiply to get 3H = 7C
Rearrange to get: 3H  7C = 0
If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7
So, (H15)/(C+15) = 13/7
Cross multiply to get 7(H15) = 13(C+15)
Expand: 7H  105 = 13C + 195
Rearrange to get: 7H  13C = 300
We now have a system of two equations and two variables:
3H  7C = 0
7H  13C = 300
Solve to get: H = 210 and C = 90
NOTE: These are the values BEFORE livestock was sold and bought.
After selling 15 horses, there are 195 horses
After buying 15 cows, there are 105 cows
After the transaction, how many more horses than cows would the farm own?
195  105 = 90
Answer: D