SOLUTION: An apple orchard contains 84 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

Algebra.Com
Question 169636: An apple orchard contains 84 trees. The number of trees per row is five more than the number of rows. Find the number of rows.
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
let x be the number of rows and y be the number of trees in each row.
:
x*y=84...eq 1
x=y+5....eq 2
:
take x's value from eq 2 and plug it into eq 1
:
(y+5)y=84
:

:
solve by quadratic formula y=7 and y =-12....throw out the negative value
:
using y's value in eq 2 we get:rows
:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=361 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7, -12. Here's your graph:
RELATED QUESTIONS

The Ortegas have an apple orchard that contains 150 trees. The number of trees in each... (answered by ewatrrr)
An apple orchard contains 85 trees. The number of trees in each row is three less than... (answered by richard1234)
An apple orchard contains 96 trees. The number of trees in each row is 4 less than twice... (answered by ewatrrr)
An apple orchard contains 84 trees. The number of trees in each row is 2 less than twice... (answered by MathTherapy,JulietG)
An apple orchard that contains 90 trees. The number of trees in each row is 3 more than... (answered by ankor@dixie-net.com)
An orchard has 1023 apple trees. The number of rows exceeds the number of trees per row... (answered by Boreal)
An orchard has 500 apple trees. The number of rows exceeds the number of trees per row by (answered by ikleyn)
A pear farm contains 126 trees. The number of trees per row is five more than the number... (answered by Stitch)
The Lassalle’s have an orange grove that contains 90 trees. The number of trees in each... (answered by richwmiller)