Denver is planting strawberry seedlings in a new garden. He can plant 3 rows of a certain length with 2 seedlings leftover or 4
1 answer:
Given:
Denver can plant 3 rows of a certain length with 2 seedlings leftover or 4 rows of the same length with 3 seedling spots left empty.
To find:
The equation for the given problem and its solution.
Solution:
Let x be the length of each row.
Denver can plant 3 rows of a certain length with 2 seedlings leftover.
Total number of seeds he has = ...(i)
Denver can plant 4 rows of the same length with 3 seedling spots left empty.
Total number of seeds he has = ...(ii)
Using (i) and (ii), we get
Isolate variable terms.
Therefore, the required equation is and the values of x is 5. Each row is 5 meters long.
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We are given sides of the triangle by expression
First side : n
Second side : m = 5n-5.
Third side : l = 5/4 m - n.
Perimeter is 90.
Therefore, first equation could be set :
n +m +l = 90 --------------equation(1)
Second equation would be
m = 5n-5 --------------equation(2)
Third equation would be
l = 5/4 m - n --------------equation(3)
Let us solve the system of equations by substitution.
Substituting m = 5n-5 and l = 5/4 m - n in first equation.
We get
n +5n-5 +5/4 m - n= 90
Now, substituting m = 5n-5 in above equation we get
n +5n-5 +5/4 (5n-5) - n= 90
5n + 25n/4 -5 - 25/4 =90
5n + 6.25n -5-6.25 = 90.
11.25n-11.25 = 90
Adding 11.25 on both sides, we get
11.25n-11.25+11.25 = 90+11.25
11.25n = 101.25.
Dividing both sides by 11.25, we get
n=9.
Plugging n=9 in 2nd equation.
m = 5(9)-5 = 45 -5 = 40.
Plugging n=9 and m=40 in first equation, we get
9 +40 +l = 90
49 +l = 90.
Subtracting 49 from both sides, we get
49-49 +l = 90-49
l = 41.
Therefore, sides are of lengths l = 41, m= 40 and n=9.
