ANSWER THIS PLEASE ASAP

a.) 72 of each type of animal, for a total of 216

b.) 16 grown cats, 4 kittens

Step-by-step explanation:

part a. It's a distribution (division) problem. The same number of each animal is distributed over some unknown number of troughs, but the total number of troughs adds up to 69. ( I hate to give this all away, as its a brilliant problem! )

Number of troughs for each animal type is How many needed by the number of animals per trough:

h/2 + c/3 + p/8 = 69  

Since we are given "the same number of horses, cows and pigs" we can substitute "x" for all.

   Get a common denominator. 24 would work, 48 also.

24x + 16x + 6x = 3372

46x = 3372    x = 72

Proof:  calculate the number of each kind of trough

Horses 72/2 = 36, Cows 72/3 = 24  Pigs 72/8 = 9    36+24+9 = 69

part b.  5c + 3k = 92,   c + k = 20  Rearrange to get a value for c to substitute.

c = 20-k   5(20-k) +3k =92  Distribute and solve

100 - 5k + 3k = 92 becomes -2k = -8  so  k = 4 Substitute into the original

c + 4 = 20  becomes c=20-4,  so c = 16

Proof: 5c +3k = 92 Substitute values 5(16) + 3(4) = 92  80 + 12 = 92

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step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3