If a certain garden plot contains 25 tomato plants, the yield per plan

Thank you so much for the solution! I was making a very silly mistake. I double checked the wording and it is identical to how it was presented on the mock exam, except for the italicization of the x in the prompt.

The question is a bit off, x is the additional plants in the area.

Easiest method to solve would be to factorise the constant given.

174 = 2*3*29

As we know plants are more than 25, and we also know plants= 25+x, produce = 10-x.

We can directly deduce the answer = 6*29 = 174. Therefore x = 4

Posted from my mobile device

Helloo. Could we map this to Focus? This question is part of FOCUS MOCK.. Yup, the wording is inaccurate


Below is the revised question -
'If a certain garden plot contains 25 tomato plants, the yield per plant will be 10 tomatoes. If the plot contains x additional plants, the yield per plant will be reduced by x tomatoes. If last year the plot contained more than 25 plants and the total yield was 174 tomatoes, how many plants did the plot contain?'

__________________
Fixed the wording. Thank you!

To solve the problem, let's translate it into mathematical terms:

1. **Initial setup**:
- The garden initially contains \( 25 \) tomato plants, and the yield per plant is \( 10 \) tomatoes, for a total yield of:
\[
25 \cdot 10 = 250 \text{ tomatoes.}
\]

2. **Changes to the setup**:
- If \( x \) additional plants are added, the total number of plants becomes \( 25 + x \).
- However, the yield per plant decreases by \( x \) tomatoes, so the new yield per plant becomes \( 10 - x \).

3. **Total yield**:
- The total yield is calculated as:
\[
\text{Total yield} = (\text{number of plants}) \cdot (\text{yield per plant}) = (25 + x)(10 - x).
\]

Expanding this, the total yield is:
\[
(25 + x)(10 - x) = 250 - 25x + 10x - x^2 = 250 - 15x - x^2.
\]

4. **Condition from the problem**:
- Last year, the plot contained more than 25 plants (\( x > 0 \)), and the total yield was \( 174 \) tomatoes. Thus, we have the equation:
\[
250 - 15x - x^2 = 174.
\]

Simplify this equation:
\[
-x^2 - 15x + 250 = 174,
\]
\[
-x^2 - 15x + 76 = 0.
\]

Multiply through by \(-1\) to simplify:
\[
x^2 + 15x - 76 = 0.
\]

5. **Solve the quadratic equation**:
Use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a},
\]
where \( a = 1 \), \( b = 15 \), and \( c = -76 \). Substituting these values:
\[
x = \frac{-15 \pm \sqrt{15^2 - 4(1)(-76)}}{2(1)} = \frac{-15 \pm \sqrt{225 + 304}}{2} = \frac{-15 \pm \sqrt{529}}{2}.
\]

Since \( \sqrt{529} = 23 \):
\[
x = \frac{-15 + 23}{2} \quad \text{or} \quad x = \frac{-15 - 23}{2}.
\]
\[
x = \frac{8}{2} = 4 \quad \text{or} \quad x = \frac{-38}{2} = -19.
\]

Since \( x > 0 \), we take \( x = 4 \).

6. **Verify the result**:
If \( x = 4 \), the total number of plants is \( 25 + 4 = 29 \), and the yield per plant is \( 10 - 4 = 6 \). The total yield is:
\[
29 \cdot 6 = 174.
\]

Thus, the plot contained **29 plants** last year.

still can't tell if 'plants' is broad (tomato plants + others) or if it's specific to only tomato plants.