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Rashid [163]
3 years ago
14

The number of cattle at 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
Mathematics
1 answer:
LuckyWell [14K]3 years ago
7 0

<span><span>let x = cows last year
</span> </span><span><span>let y = bulls last year
</span> </span><span><span>x + y = last years total
</span> </span><span><span>0.9x + 1.5y = 660 (this year's total)
</span> <span>1.1(x+y) = 660  </span>= </span><span>1.1x + 1.1y = 660
</span><span>
</span><span><span>so:
</span> </span><span><span>0.9x + 1.5y = 1.1x + 1.1y
</span> </span><span><span>subtract 0.9x from each side:
</span> </span><span><span>1.5y = 0.2x + 1.1y
</span> </span><span><span>subtract 1.1y from each side
</span> </span><span><span>0.4y = 0.2x
</span> </span><span><span>to make x 1 multiply both sides by 5
</span> </span><span><span>2y = x
</span> </span><span><span>substitute for x in one of the original problems:
</span> since they had 660 this year and that number is 10% higher than last year, then we had 600 total last year. </span>

<span><span>So:
</span> </span><span><span>600 = x + y
</span> </span><span><span>substitute into that one with the 2y = x
</span> </span><span><span>600 = 2y + y
</span> </span><span><span>600 = 3y
</span> </span><span><span>200 = y
</span> </span><span><span>then 600 - y = x
</span> </span><span><span>so 600 - 200 = x
</span> 400 = x</span>

<span> So you had 400 cows and 200 bulls last year</span>


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