SOLUTION: The Lassalle’s have an orange grove that contains 90 trees. The number of trees in each row is 3 more than twice the number of rows. Find the number of rows and the number of tree

Algebra.Com
Question 885700: The Lassalle’s have an orange grove that contains 90 trees. The number of trees in each row is 3 more than twice the number of rows. Find the number of rows and the number of trees per row.
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
90=(2x+3)*x
2x^2+3x-90=0
we want factors of -180 which add to 3
x=6
2x+3=15
6 rows with 15 trees in each row.
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?



To find these two numbers, we need to list all of the factors of (the previous product).



Factors of :

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-30,-36,-45,-60,-90,-180



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to .

1*(-180) = -180
2*(-90) = -180
3*(-60) = -180
4*(-45) = -180
5*(-36) = -180
6*(-30) = -180
9*(-20) = -180
10*(-18) = -180
12*(-15) = -180
(-1)*(180) = -180
(-2)*(90) = -180
(-3)*(60) = -180
(-4)*(45) = -180
(-5)*(36) = -180
(-6)*(30) = -180
(-9)*(20) = -180
(-10)*(18) = -180
(-12)*(15) = -180


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-1801+(-180)=-179
2-902+(-90)=-88
3-603+(-60)=-57
4-454+(-45)=-41
5-365+(-36)=-31
6-306+(-30)=-24
9-209+(-20)=-11
10-1810+(-18)=-8
12-1512+(-15)=-3
-1180-1+180=179
-290-2+90=88
-360-3+60=57
-445-4+45=41
-536-5+36=31
-630-6+30=24
-920-9+20=11
-1018-10+18=8
-1215-12+15=3




From the table, we can see that the two numbers and add to (the middle coefficient).



So the two numbers and both multiply to and add to



Now replace the middle term with . Remember, and add to . So this shows us that .



Replace the second term with .



Group the terms into two pairs.



Factor out the GCF from the first group.



Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



Combine like terms. Or factor out the common term



===============================================================



Answer:



So factors to .



In other words, .



Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
RELATED QUESTIONS

The Ortegas have an apple orchard that contains 150 trees. The number of trees in each... (answered by ewatrrr)
An apple orchard that contains 90 trees. The number of trees in each row is 3 more than... (answered by ankor@dixie-net.com)
Please Help! 1). The Ortegas have an apple orchard that contains 90 trees. The number... (answered by ankor@dixie-net.com)
An apple orchard contains 96 trees. The number of trees in each row is 4 less than twice... (answered by ewatrrr)
An orchard has 864 orange trees. The number of rows exceeds the number of trees per row... (answered by ikleyn)
an orchid has 672 orange trees. The number of rows exceeds the number of trees per row by (answered by josmiceli)
An apple orchard contains 85 trees. The number of trees in each row is three less than... (answered by richard1234)
An apple orchard contains 84 trees. The number of trees per row is five more than the... (answered by Mathtut)
Samuel is planting trees. He has enough trees to plant 6, 7, or 14 trees in each row.... (answered by solver91311)