Question

A vineyard has 145 acres of Chardonnay grapes. A particular soil supplement requires 5.50 grams for every square meter of vineyard. How many kilograms of the soil supplement are required for the entire vineyard? Given that 1 km2 = 247 acres. Express your answer in kilograms to three significant figures.

Answer 1

3230 kilograms of the soil supplement are required for the entire vineyard

Further explanation

Some units that need to be recalled are as follows :

1 km = 1000 m = 10³ m

1 km² = 1000000 m² = 10⁶ m

1 km² = 247 acres

1 kg = 1000 g

Let's tackle the problem now!

A vineyard has 145 acres of Chardonnay grapes.

$145 ~ acres = \frac{145}{247} \times 1 ~ km^2$

$145 ~ acres = \frac{145}{247} ~ km^2$

$\boxed {145 ~ acres \approx 0.587 ~ km^2}$

A particular soil supplement requires 5.50 grams for every square meter of vineyard.

$1 ~ m^2 \rightarrow 5.50 ~ gram$

$1 ~ km^2 = 10^6 ~ m^2 \rightarrow 5.50 \times 10^6 ~ gram$

$1 ~ km^2 \rightarrow 5.50 \times 10^6 \times 10^{-3} ~ kg$

$\boxed {1 ~ km^2 \rightarrow 5.50 \times 10^3 ~ kg}$

$145 ~ acres = \frac{145}{247} ~ km^2 \rightarrow \frac{145}{247} \times 5.50 \times 10^3 ~ kg$

$145 ~ acres \rightarrow \frac{797500}{247} ~ kg$

$145 ~ acres \rightarrow 3230 ~ kg$

Conclusion :

It required 797500/247 kg ≈ 3230 kg of the soil supplement for the entire vineyard

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic

Keywords: Addition , Subtraction , Multiplication , Division , Number , Expression , Time , Duration , Write

Answer 2

The amount of the soil supplement is required for the entire vineyard $\boxed{3230{\text{ kilogram}}}.$

Further explanation:

Given:

A vineyard has 145 acres of Chardonnay grapes.

A particular soil supplement requires 5.50 grams for every square meter of vineyard.

$\boxed{1{\text{ k}}{{\text{m}}^{\text{2}}} = 247{\text{ acres}}}$

Explanation:

A vineyard has 145 acres of Chardonnay grapes.

Convert 145 acres in $k{m^2}.$

$\begin{aligned}145{\text{ acres}}&= \frac{{145}}{{247}} \times {\text{ 1 k}}{{\text{m}}^2}\\&= 0.587{\text{ k}}{{\text{m}}^2}\\\end{aligned}$

In $1{\text{ }}{{\text{m}}^2}$ area the amount of soil supplement requires is $5.5{\text{ gram}}.$

$1{\text{ }}{{\text{m}}^2} \to 5.50{\text{ gram}}$

In $1{\text{ k}}{{\text{m}}^2}$ the required amount of soil supplement can be calculated as follows,

$1{\text{ k}}{{\text{m}}^2} = 5.50 \times {10^3}{\text{ kg}}$

The amount of soil supplement required for $145{\text{ acres}}$ of land can be calculated as follows,

$\begin{aligned}{\text{Soil supplement}} &= \frac{{145}}{{247}} \times 5.50 \times {10^3}{\text{ kg}}\\{\text{ }}&=\frac{{797500}}{{247}}{\text{ kg}}\\&= 3230{\text{ kg}}\\\end{aligned}$

The amount of the soil supplement is required for the entire vineyard $\boxed{3230{\text{ kilogram}}}.$

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Unit Conversion

Keywords: vineyard, 145 acres, Chardonnay grapes, particular soil, supplement, 5.50 grams, square meter of vineyard, kilograms, entire vineyard, significant figures, three significant figures, 1 km2 = 247 acres,