The Ortegas have an apple orchard that contains 70 trees. The number of trees in each row is 4 more than twice the number of rows. Find the number of rows and the number of trees per row.
A) 5 rows with 9 trees per row
B) 9 rows with 14 trees per row
C) 5 rows with 14 trees per row

Question

Quizplus · Accepted Answer

Let x be the number of rows and y be the number of trees per row. Then we have the equations:

xy = 70  (the total number of trees)
y = 2x + 4  (the number of trees per row is 4 more than twice the number of rows)

Substituting the second equation into the first equation, we get:

x(2x + 4) = 70
2x^2 + 4x - 70 = 0
x^2 + 2x - 35 = 0
(x + 7)(x - 5) = 0
x = -7 or x = 5

Since we can't have a negative number of rows, we choose x = 5. Substituting this into the equation y = 2x + 4, we get y = 14. Therefore, there are 5 rows with 14 trees per row.

The Ortegas Have an Apple Orchard That Contains 70 Trees