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Question 849811: On Monday, the park was billed $315 to feed 21 coyotes and 21 lions. On Tuesday, the park was billed $484 to feed 28 coyotes and 36 lions. What is the cost to feed each lion and each coyote?
You get a notification that next week, the prices to feed both animals will increase by 5%. What will be the cost to feed 35 coyotes and 40 lions?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = cost to feed coyotes and y = cost to feed lions.
on wednesday, 21x + 21y = 315
on tuesday, 28x + 36y = 484
solve these 2 equations simultaneously to find the value of x and y.
equations are:
21x + 21y = 315
28x + 36y = 484
you can solve by substitution, or by elimination, or by graphing.
i'll solve by elimination.
least common multiple of 21 and 28 is 84.
multiply first equation by 4 and second equation by 3 to get:
84x + 84y = 1260
84x + 108y = 1452
subtract first equation from the second to get:
24y = 192
divide 192 by 24 to get:
y = 8
now that you know the value of y, substitute for y in either equation to find the value of x.
substituting in 21x + 21y = 315 gets:
21x + 21(8) = 315
simplify to get:
21x + 168 = 315
subtract 168 from both sides of the equation to get:
21x = 147
divide both sides of the equation by 21 to get:
x = 7
your answer should be:
x = 7 = cost to feed one coyote.
y = 8 = cost to feed one lion.
confirm this solution is correct by substituting for x and y in both equations.
both original equations are:
21x + 21y = 315
28x + 36y = 484
after substituting, these equations become:
21(7) = 21(8) = 315
28(7) + 36(8) = 484
evaluate both equations to get:
315 = 315
484 = 484
the solution is confirmed to be good.
x = 7
y = 8
cost to feed one coyote = 7.
cost to feed one lion = 8.
if the price is increased by 5%, then:
cost to feed one coyote becomes 7 + .05*7 = 7.35
cost to feed one lion becomes 8 + .05*8 = 8.4.
the cost to feed 35 coyotes and 40 lions then becomes:
35(7.35) + 40(8.4) = 593.25
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