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solve each problem that has a solution.If a problem has no solution, explain why
1. Lee and Jessie swam towards each other from opposite sides of a lake that is 3.9
km wide.They began swimming a 2:00P.M. and met a 2:30 P.M. Lee's speed was
1 km/h greater than jessies speed . Find their speeds.
2. A rectangle is 4 cm longer than it is wide . If the length and width are both decreased by 2cm , the area is decreased by 24 cm^2. Find the dimensions of the original rectangle .
3. Roy says he has more nickels than dimes . If he has $5.20, how many of each coin does he have ?

Respuesta :

nobillionaireNobley
2. Let the length of the rectangle be x cm and the width = (x - 4) cm. Area = x(x - 4) = (x^2 - 4x) cm^2
If the length and the width are both decreased by 2cm, new length = (x - 2) cm and new width = (x - 4 - 2) = (x - 6) cm. New area = (x - 2)(x - 6) = (x^2 - 8x + 12) cm^2
Original area - 24cm^2 = new area
x^2 - 4x - 24 = x^2 - 8x + 12
-4x + 8x = 12 + 24
4x = 36
x = 36/4 = 9cm
Therefore the original length of the rectangle = 9cm while the original width is 9 - 4 = 5 cm.
younglargeamount

2. Let the length of the rectangle be x cm and the width = (x - 4) cm. Area = x(x - 4) = (x^2 - 4x) cm^2

If the length and the width are both decreased by 2cm, new length = (x - 2) cm and new width = (x - 4 - 2) = (x - 6) cm. New area = (x - 2)(x - 6) = (x^2 - 8x + 12) cm^2

Original area - 24cm^2 = new area

x^2 - 4x - 24 = x^2 - 8x + 12

-4x + 8x = 12 + 24

4x = 36

x = 36/4 = 9cm

Therefore the original length of the rectangle = 9cm while the original width is 9 - 4 = 5 cm.

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