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 Question from Jessica, a student: You have exactly $\$100.00$to spend. You must get 100 animals. The chicks cost$\$0.10$ each. The pigs cost $\$2.00$each. The sheep cost$\$5.00$ each. You must get some of each animal. How many of each animal can you get?

Hi Jessica,

Solving this problem involves some guess and check but a little algebra can reduce the amount of guessing and checking.

Suppose the number of chicks purchased is $C,$ the number of pigs purchased is $p$ and the number of sheep purchased is $s.$ Since the total number of animals purchased is 100 you know that

$c + p + s = 100.$

You also know that the total cost was $\$100$and hence $0.1 c + 2 p + 5 s = 100.$ Multiplying the second equation by$10$and subtracting the first equation from the result yields $19 p + 49 s = 900$ or $19 p = 900 - 49s.$$s$and$p$are positive integers and$s$can't be larger then 18. Do you see why? Now comes the guess and check. Try possible values of$s$until you find an$s$so that$900 - 49s$is a multiple of 19. Does this value of$s\$ give you a solution to the problem?

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.