There are 648 cows and sheep on a farm. The ratio of the number of cows to the number of sheep is 5:4. At an auction, 2/3 of the sheep and some cows are sold. The ratio of the number of cows to the number of sheep left is no 3:1. How many cows are sold?
Is the answer 144?
X sheep.
5x/4 cows.
x + 5x/4 = 648,
4x + 5x = 2592,
X = 288.
5x/4 = 360.
After the auction:
288/3 = 96 sheep left.
Cows left = 3 * 96 =
Woo Wee! Love this question!
It is going to be part of a grade 9 math assignment in this coming week.
Thank-you Indiana Jones for sharing : )
And thank-you henry2 and oobleck for 2 different solutions (than mine : )
this is 9th grade math????!!!!
Nope. Too bad you didn't show your work...
c+s = 648
c/s = 5/4
If x cows are sold then
(c-x)/(s/3) = 3/1
Cows sold = 360 - cows left.
2wedrf
To find out how many cows are sold, we'll need to break down the problem step by step.
Step 1: Let's assign variables to the number of cows and sheep on the farm.
Let's call the number of cows "C" and the number of sheep "S". From the problem statement, we know that:
C + S = 648
Step 2: Determine the ratio between the number of cows and sheep on the farm.
We're given that the ratio of cows to sheep is 5:4. This means that the number of cows can be represented by 5x, and the number of sheep can be represented by 4x, where x is a common factor.
Cows:Sheep = 5:4
C = 5x
S = 4x
Step 3: Use the ratio to find the value of x.
Since we know the total number of animals on the farm is 648, we can set up an equation using the values we found in step 2:
5x + 4x = 648
9x = 648
x = 72
Step 4: Calculate the number of cows and sheep using the value of x.
Now that we know x, we can substitute it back into our equations from step 2:
C = 5x = 5 * 72 = 360
S = 4x = 4 * 72 = 288
So, there are 360 cows and 288 sheep on the farm.
Step 5: Determine how many animals are sold at the auction.
We're told that 2/3 of the sheep and some cows are sold. Let's represent the number of cows sold as "C'". We'll also represent the number of sheep sold as "S'". The remaining number of cows and sheep after the auction can be represented as "C''" and "S''", respectively.
From the given information, we have:
C'' + S'' = (C - C') + (S - S')
Step 6: Use the information on the remaining ratio to set up an equation.
We're told that the ratio of the number of cows to the number of sheep left is now 3:1. This means that we can represent the remaining number of cows as 3y and the remaining number of sheep as y, where y is a common factor.
C'' = 3y
S'' = y
Step 7: Set up an equation using the equation from step 5 and the values from step 6.
C'' + S'' = (C - C') + (S - S')
3y + y = (360 - C') + (288 - S')
Step 8: Simplify and solve for C':
4y = (360 - C') + (288 - S')
4y = 648 - (C' + S')
Since we're trying to find the number of cows sold (C'), let's isolate C':
C' = 648 - 4y
Step 9: Determine the value of y.
Since we know C' + S' (the total number of animals sold at the auction) is equal to 2/3 of the total number of sheep (2/3 * 288 = 192), we have:
C' + S' = 192
Substituting the value of C':
648 - 4y + y = 192
3y = 648 - 192
3y = 456
y = 152
Step 10: Calculate the number of cows sold (C').
Substituting the value of y into the equation we found in step 8:
C' = 648 - 4 * 152
C' = 648 - 608
C' = 40
Therefore, the number of cows sold at the auction is 40, not 144.