SOLUTION: Hi farm animals are for sale in groups of five.100 animals were bought for 1000 dollars.a pig cost 20 dollars, chicken 5 dollars and a sheep 30 dollars.how many sheep were bought.

Let number of groups of pigs, chickens, and sheep purchased, be P, C, and S, respectively

Then: 5P + 5C + 5S = 100______5(P + C + S) = 5(20)_______P + C + S = 20______P = 20 – C - S ---- eq (i)

Also, 20(5P) + 5(5C) + 30(5S) = 1,000______100P + 25C + 150S = 1,000_____25(4P + C + 6S) = 25(40)_______4P + C + 6S = 40 -------- eq (ii)

4(20 – C – S) + C + 6S = 40 ------- Substituting 20 – C – S for P in eq (ii)

80 – 4C – 4S + C + 6S = 40

6S – 4S – 4C + C = 40 – 80

2S – 3C = - 40

3C = 2S + 40





As a sheep is the costliest, and are in groups of 5, we can begin by determining the most number of sheep that could’ve been purchased

Since 1 sheep costs $30, neither 8 groups (40 sheep) nor 7 groups (35 sheep) can be purchased, as they'd cost $1,200, and $1,050, respectively



Therefore, by letting the number of groups of sheep that were purchased be 6, 5, 4, 3, 2, 1, and 0, and by using the above

equation: , we find that:

Case 1:

4 groups of sheep, or 4(5), or 20 sheep for 20(30), or $600 can be purchased

16 groups of chicken, or 16(5), or 80 chickens, for 80(5), or $400 can be purchased

0 groups of pigs, or 0(5), or 0 pigs, for 0(20), or $0 can be purchased

This results in a total of: 20 (4 + 16) groups of 5, totaling 100 (20 + 80) animals for $1,000 (600 + 400)



Case 2:

1 group of sheep, or 1(5), or 5 sheep for 5(30), or $150, can be purchased

14 groups of chicken, or 14(5), or 70 chickens, for 70(5), or $350, can be purchased

5 groups of pigs, or 5(5), or 25 pigs, for 25(20), or $500, can be purchased

This results in a total of: 20 (1 + 14 + 5) groups of 5, totaling 100 (5 + 70 + 25) animals for $1,000 (150 + 350 + 500)