SOLUTION: Please Help! 1). The Ortegas have an apple orchard that contains 90 trees. The number of trees in each row is 3 more that twice the number of rows. Find the nmber of rows and th

Click here to see ALL problems on Miscellaneous Word Problems

Question 138319: Please Help!
1). The Ortegas have an apple orchard that contains 90 trees. The number of trees in each row is 3 more that twice the number of rows. Find the nmber of rows and the number of trees per row?
2). The area of the floor of the rectangle room is 175 square feet. The lenght of the room if 1 1/2 feet longer than the width. Find the length of the room.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
1). The Ortegas have an apple orchard that contains 90 trees. The number of trees in each row is 3 more that twice the number of rows. Find the number of rows and the number of trees per row?
:
Let x = no. of rows
It says,"The number of trees in each row is 3 more that twice the number of rows."
No. trees in each row = (2x+3)
:
From what is says, we can say,"The number of rows times the no. of trees in each row = 90
:
x * (2x+3) = 90
2x^2 + 3x - 90 = 0; a quadratic equation
Factors to:
(2x + 15)(x - 6) = 0
the positive solution;
x = 6 rows
then
2(6) + 3 = 15 in each row; checks out 6 * 15 = 90
:
:
2). The area of the floor of the rectangle room is 175 square feet. The length of the room if 1 1/2 feet longer than the width. Find the length of the room.
:
Let x = width of the room
It says,"the length of the room if 1 1/2 feet longer than the width.: therefore:
L = (x + 1.5)
:
Area = L * x, substitute (x+1.5) for L:
(x+1.5) * x = 175
x^2 + 1.5x - 175 = 0; our old friend, the quadratic equation again.
:
2x^2 + 3x - 350 = 0 multiplied by 2 to get rid of that fraction
factors to:
(2x - 25)(x + 14) = 0
The positive solutionL
2x = + 25
x =
x = 12.5 ft is the width
then
12.5 + 1.5 = 14 ft is the length
;
Check by finding the area: 12.5 * 14 = 175