I do apologize for posting so many questions, but my real problemin math is stor

Question

I do apologize for posting so many questions, but my real problemin math is story problemsand really grasping how to set them up and form anequation. I do have a few more questions, but all I need isthe initial set-up and how I may form those into an equation. Thank you very much
1. The perimeter of a rectangle is 32 inches and its area is63 square inches. Find the length and width of the rectangle.
2. A rancher bought some calves for 170$ each. "Jet Age"rustlers stole 6 of them. Four months later, the rancher soldthe remaining calves for 240$ each. He paid a feed billof 400$ and still made a profit of 4111$. How many calves did hebuy. Hint: Selling price-cost=profit.
1. The perimeter of a rectangle is 32 inches and its area is63 square inches. Find the length and width of the rectangle.
2. A rancher bought some calves for 170$ each. "Jet Age"rustlers stole 6 of them. Four months later, the rancher soldthe remaining calves for 240$ each. He paid a feed billof 400$ and still made a profit of 4111$. How many calves did hebuy. Hint: Selling price-cost=profit.

Explanation / Answer

1. Let x and y be the sides of the rectangle. Now Perimeter=2x+2y=32 and Area=xy=63 Now you have two equation in two unknowns. Sox=63/y from Area equation. Now substitute for x inPerimeter equation and solve for y. Once you have y you canfind x using either equation. 2(63/y)+2y=32
126/y+2y=32
126+2y^2=32y
2y^2-32y+126=0
2(y^2-16y+63)=0
2(y-9)(y-7)=0
y=9, y=7
x7=63
x=9
x9=63
x=7
2. Let c be the number of cows he bought. His total cost is T=$170c+400 He sold c-6 for $240 each and had a net profit of $4111 Hence, $240(c-6)-T=4111 240(c-6)-170c-400=4111 Solve for c.
240c-1440-170c-400=4111
70c-1840=4111
70c=5951
c=5951/70
c=85.01
so he bought 85 cows

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