Question

finding a total cost

katherine is landscaping her home with juniper trees and pansies. she wants to arrange 15 pansies around each of 8 trees. each tree costs \\$20.75 and a six-pack of pansies costs \\$2.50. explain how to write an expression to find katherines final cost.

Explanation:

Calculate the total cost of the trees

Using the Writing Expressions knowledge point

$$ \text{Cost of trees} = 8 \times 20.75 $$

Determine the total number of pansies needed

Using the Writing Expressions knowledge point

$$ \text{Total pansies} = 8 \times 15 $$

Determine the number of six-packs of pansies to buy

Using the Writing Expressions knowledge point

$$ \text{Number of six-packs} = \frac{8 \times 15}{6} $$

Calculate the total cost of the pansies

Using the Writing Expressions knowledge point

$$ \text{Cost of pansies} = \frac{8 \times 15}{6} \times 2.50 $$

Combine the costs to write the final expression

Using the Writing Expressions knowledge point

$$ \text{Total Cost} = 8 \times 20.75 + \frac{8 \times 15}{6} \times 2.50 $$

Answer:

To find Katherine's final cost, write an expression that combines the total cost of the trees and the total cost of the pansies:

1. Cost of the trees: Multiply the number of trees by the cost per tree:

$$8 \times 20.75$$

1. Cost of the pansies:

• Find the total number of pansies needed by multiplying the number of trees by the pansies per tree: \(8 \times 15\).
• Divide this total by \(6\) to find the number of six-packs needed: \(\frac{8 \times 15}{6}\).
• Multiply the number of six-packs by the cost per pack (\(2.50\)): \(\frac{8 \times 15}{6} \times 2.50\).

Combining these two parts, the final expression is:

$$8 \times 20.75 + \frac{8 \times 15}{6} \times 2.50$$