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storchak [24]
2 years ago
8

Write a system of two equations in two variables to solve the problem. when fully extended, a ladder is 28 feet in length. if th

e extension is 4 feet shorter than the base, how long is each part of the ladder? base
Mathematics
1 answer:
Alisiya [41]2 years ago
5 0
Let the base of the ladder be x ft and the extension be y ft.

"when fully extended, a ladder is 28 feet in length."

means: x+y=28

"<span>the extension is 4 feet shorter than the base</span>"

means: y=x-4,   that is x-y = 4, (taking y to the side of x, and -4 to the other side of x and y)

thus, we have the system of equations:

1) x+y= 28 

2) x-y=4

adding the 2 equations, we have:

(x+y)+(x-y)=28+4

2x=32

x=32/2=16


x+y=28, so 16+y=28, thus y=12


Answer: Base: 16, Extension 12
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