SOLUTION: The number of cattle on a farm is 660. This is a 10% decrease in the number of cows, a 50% increase in the number of bulls, and an overall increase of 10% in the total number of ca

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The number of cattle on a farm is 660. This is a 10% decrease in the number of cows, a 50% increase in the number of bulls, and an overall increase of 10% in the total number of ca      Log On


   

Question 1184830: The number of cattle on a farm is 660. This is a 10% decrease in the number of cows, a 50% increase in the number of bulls, and an overall increase of 10% in the total number of cattle from last year. How many cows and bulls were there each at the farm last year?
Answer by greenestamps(13200) About Me  (Show Source):
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The total number of cattle, 660, is an increase of 10% over the total last year:

660+=+1.10x
x=660%2F1.10=600

The total number of cattle last year was 600.

The total of 660 is an decrease in 10% of the number of cows and an increase of 50% in the number of bulls.

Let c and b be the numbers of cows and bulls last year. Then

(1) the total number of cattle last year was 600:
c%2Bb=600

(2) the total number this year is 660:
0.9c%2B1.5b=660

Multiply (2) by 10 to get rid of the decimals
9c%2B15b=6600

Multiply (1) by 9 to eliminate c:
9c%2B9b=5400
6b=1200
b=200

ANSWERS: The number of bulls at the farm last year was b=200; the number of cows at the farm last year was 600-200=400.