An orchard has enough space to plant 21 rows with y trees in each row, or 18 rows with y+7 trees in each row. If each orchard plan contains the same number of trees, how many trees can each orchard contain?

Question

An orchard has enough space to plant 21 rows with y trees in each row, or 18 rows with y+7 trees in each row. If each orchard plan contains the same number of trees, how many trees can each orchard contain?

*I know the answer is 882 trees. But, I have no idea how to set up the problem so that I can solve it. Please help. Thank you.

Answer 1

Thank you!

21y

21 X 42= 882

I get it! Thank you!

Answer 2

since (21)(y) is the same as 18(y+7) , let's say so:

21y = 18(y+7)
21y = 18y + 126
3y = 126
y = 42

so ......

Answer 3

Let's break down the problem step-by-step.

Step 1: Assign values to unknowns.
Let's assume that the number of trees in each row is represented by 'y'.

Step 2: Express the given information mathematically.
- According to the problem, an orchard can have 21 rows with 'y' trees in each row, or it can have 18 rows with 'y + 7' trees in each row.
- We can write these statements as equations:
orchard 1: 21y
orchard 2: 18(y + 7)

Step 3: Set up an equation to find the number of trees in each orchard.
Since the number of trees is the same for both orchards, we can write the equation: 21y = 18(y + 7).

Step 4: Solve the equation.
Let's solve the equation:
21y = 18(y + 7)

Expanding the equation:
21y = 18y + 126

Combining like terms:
21y - 18y = 126
3y = 126

Dividing both sides by 3:
y = 42

Step 5: Calculate the total number of trees in each orchard.
Now that we have the value of 'y', we can substitute it back into either equation to find the total number of trees in each orchard.

Let's substitute it into the equation for orchard 1: 21y = 21(42) = 882.

Therefore, each orchard can contain 882 trees.

Answer 4

Let's set up the problem step by step:

We are given two equations based on the information given in the question:

1) Equation 1: The orchard can plant 21 rows with y trees in each row.

2) Equation 2: The orchard can plant 18 rows with y+7 trees in each row.

To find out how many trees each orchard can contain, we need to solve for y, the number of trees in each row.

Step 1: Set up Equation 1:
The orchard can plant 21 rows with y trees in each row, so the total number of trees in Equation 1 is 21y.

Step 2: Set up Equation 2:
The orchard can plant 18 rows with y+7 trees in each row, so the total number of trees in Equation 2 is 18(y+7).

Step 3: Set the equations equal to each other:
Since both equations represent the same orchard, we can set Equation 1 equal to Equation 2:
21y = 18(y+7).

Step 4: Solve for y:
Now, we'll solve the equation to find the value of y:
21y = 18y + 18(7)
21y = 18y + 126
21y - 18y = 126
3y = 126
y = 126/3
y = 42.

Step 5: Find the total number of trees in the orchard:
Now that we know the value of y, we can substitute it into either equation to find the total number of trees.

Using Equation 1:
Total number of trees = 21y = 21 * 42 = 882 trees.

Therefore, each orchard can contain 882 trees.