Answer :
Sure! Let's solve the problem step by step:
a. Write a linear equation in standard form to represent the situation.
The plot is 16 by 25 feet, giving it a total area of [tex]\(16 \times 25 = 400\)[/tex] square feet. Each tomato plant needs 8 square feet, and each pepper plant needs 5 square feet. We can write an equation to represent the number of tomato plants (x) and pepper plants (y) that can be planted using all 400 square feet of space:
[tex]\[ 8x + 5y = 400 \][/tex]
b. If you only grow pepper plants, how many can you plant?
If you decide to grow only pepper plants, each requiring 5 square feet, you can use the entire 400 square feet for them. The maximum number of pepper plants you can plant is calculated by dividing the total area by the space each pepper plant needs:
[tex]\[ \text{Maximum pepper plants} = \frac{400}{5} = 80 \][/tex]
So, you can plant 80 pepper plants.
c. If you only grow tomato plants, how many can you plant?
If you grow only tomato plants, and each requires 8 square feet, divide the total area by the space each tomato plant needs:
[tex]\[ \text{Maximum tomato plants} = \frac{400}{8} = 50 \][/tex]
So, you can plant 50 tomato plants.
d. How many pepper plants can you grow if you have 15 tomato plants?
First, calculate the space used by the 15 tomato plants:
[tex]\[ \text{Area used by tomato plants} = 15 \times 8 = 120 \text{ square feet} \][/tex]
Subtract the area used by tomato plants from the total area to find the remaining area available for pepper plants:
[tex]\[ \text{Remaining area} = 400 - 120 = 280 \text{ square feet} \][/tex]
Now, calculate how many pepper plants can be planted in the remaining area:
[tex]\[ \text{Pepper plants with 15 tomatoes} = \frac{280}{5} = 56 \][/tex]
So, with 15 tomato plants, you can plant 56 pepper plants.
I hope this helps! If you have any more questions, feel free to ask.
a. Write a linear equation in standard form to represent the situation.
The plot is 16 by 25 feet, giving it a total area of [tex]\(16 \times 25 = 400\)[/tex] square feet. Each tomato plant needs 8 square feet, and each pepper plant needs 5 square feet. We can write an equation to represent the number of tomato plants (x) and pepper plants (y) that can be planted using all 400 square feet of space:
[tex]\[ 8x + 5y = 400 \][/tex]
b. If you only grow pepper plants, how many can you plant?
If you decide to grow only pepper plants, each requiring 5 square feet, you can use the entire 400 square feet for them. The maximum number of pepper plants you can plant is calculated by dividing the total area by the space each pepper plant needs:
[tex]\[ \text{Maximum pepper plants} = \frac{400}{5} = 80 \][/tex]
So, you can plant 80 pepper plants.
c. If you only grow tomato plants, how many can you plant?
If you grow only tomato plants, and each requires 8 square feet, divide the total area by the space each tomato plant needs:
[tex]\[ \text{Maximum tomato plants} = \frac{400}{8} = 50 \][/tex]
So, you can plant 50 tomato plants.
d. How many pepper plants can you grow if you have 15 tomato plants?
First, calculate the space used by the 15 tomato plants:
[tex]\[ \text{Area used by tomato plants} = 15 \times 8 = 120 \text{ square feet} \][/tex]
Subtract the area used by tomato plants from the total area to find the remaining area available for pepper plants:
[tex]\[ \text{Remaining area} = 400 - 120 = 280 \text{ square feet} \][/tex]
Now, calculate how many pepper plants can be planted in the remaining area:
[tex]\[ \text{Pepper plants with 15 tomatoes} = \frac{280}{5} = 56 \][/tex]
So, with 15 tomato plants, you can plant 56 pepper plants.
I hope this helps! If you have any more questions, feel free to ask.
