Question 2

Rani has an empty rectangular plot of land behind her house measuring $1 \text{ m} \times 0.35 \text{ m}$ that can be planted with various types of fruit seedlings. Rani bought a package of fruit seedlings consisting of 2 strawberry seedlings, 1 orange seedling, and 4 mango seedlings for $\text{Rp}45,000.00$ . Planting one strawberry seedling requires a land area of $10 \text{ cm} \times 5 \text{ cm}$ , and planting one orange seedling requires twice the land area needed for one strawberry seedling.

It is known that planting one mango seedling requires a land area of $5 \text{ cm} \times 2.5 \text{ cm}$ . If Rani wants to buy two packages of fruit seedlings and fertilizer for the land to be planted with seedlings at a price of $\text{Rp}100,000.00/\text{m}^2$ , then the total amount of money Rani has to spend is ....

$\text{Rp}95,000.00$

$\text{Rp}96,000.00$

$\text{Rp}97,000.00$

$\text{Rp}98,000.00$

$\text{Rp}99,000.00$

Explanation

We will calculate the total cost required by Rani, which consists of the purchase price of the seedling packages and the cost of fertilizer for the land used.

Determining the Number of Seedlings

Rani buys 2 packages of fruit seedlings. Each package contains 2 strawberry seedlings, 1 orange seedling, and 4 mango seedlings. Thus, the total seedlings obtained from 2 packages are:

Strawberry: $2 \times 2 = 4$ seedlings.
Orange: $2 \times 1 = 2$ seedlings.
Mango: $2 \times 4 = 8$ seedlings.

Calculating the Required Land Area

We calculate the land area for each type of seedling:

Strawberry Seedlings

The land size for one strawberry seedling is $10 \text{ cm} \times 5 \text{ cm}$ .

L_{\text{strawberry}} = 10 \times 5 = 50 \text{ cm}^2

Total area for 4 strawberry seedlings:

L_{\text{total strawberry}} = 4 \times 50 = 200 \text{ cm}^2

Orange Seedlings

The land size for an orange seedling is twice the size of the land for a strawberry seedling. In this context, the length and width dimensions are each doubled ( $20 \text{ cm} \times 10 \text{ cm}$ ).

L_{\text{orange}} = 20 \times 10 = 200 \text{ cm}^2

Total area for 2 orange seedlings:

L_{\text{total orange}} = 2 \times 200 = 400 \text{ cm}^2

Mango Seedlings

The land size for one mango seedling is $5 \text{ cm} \times 2.5 \text{ cm}$ .

L_{\text{mango}} = 5 \times 2.5 = 12.5 \text{ cm}^2

Total area for 8 mango seedlings:

L_{\text{total mango}} = 8 \times 12.5 = 100 \text{ cm}^2

Total Land Area

L_{\text{total}} = 200 + 400 + 100

L_{\text{total}} = 700 \text{ cm}^2

We convert the area unit to square meters ( $1 \text{ m}^2 = 10,000 \text{ cm}^2$ ):

L_{\text{total}} = \frac{700}{10,000} = 0.07 \text{ m}^2

Calculating Total Cost

Seed Cost

The price of 1 package is $\text{Rp}45,000.00$ . For 2 packages:

\text{Seed Cost} = 2 \times 45,000 = \text{Rp}90,000.00

Fertilizer Cost

The price of fertilizer is $\text{Rp}100,000.00/\text{m}^2$ . For land with an area of $0.07 \text{ m}^2$ :

\text{Fertilizer Cost} = 0.07 \times 100,000 = \text{Rp}7,000.00

Total Expenditure

\text{Total} = 90,000 + 7,000

\text{Total} = 97,000

So, the amount of money Rani has to spend is $\text{Rp}97,000.00$ .

Command Palette

Number 2

Explanation

Determining the Number of Seedlings

Calculating the Required Land Area

Calculating Total Cost