An interior decorator wants to complete a sunroom with three types of plants: Kentia Palm plants, Schefflera plants, and Areca Palm plants. Each Kentia Palm plant costs $45, each Schefflera plant costs $35, and each Areca Palm plant costs $40. The decorator plans to buy 10 plants. Let k be the number of Kentia Palm plants and s be the number of Schefflera plants the decorator buys. In terms of k and s, how many Areca Palm plants does the decorator buy?

Step-by-step explanation:

Kentia Palm plant = $45, Schefflera plant = $35

Areca Palm plant = $40

The decorator plans to buy 10 plants.

A.) Let k be the number of kentia palm plants and s be the number of schefflera plants the decorator buys. In terms of k and s, how many Areca Palm plants does the decorator buy?

k = number of kentia palm plants s = number of schefflera plants

Number of Areca Palm plants = total number of plants - (number of kentia palm plants + number of schefflera plants

= 10 - (k + s)

Number of Areca Palm plants, a = 10 - (k + s)

B.) write and simplify an expression in term of k and s for the total cost of the plants.

Total cost = 45k + 35s + 40a

Substitute a = 10 - (k + s)

Total cost = 45k + 35s + 40{10 - (k + s)

= 45k + 35s + 40(10 - k + s)

= 45k + 35s + 400 - 40k + 40s

= 5k + 75s + 400

Total cost = 5k + 75s + 400

C.) Of the 10 plants the decorator buys, 2 are kentia palm plants and 5 are schefflera plants. Use your expression from part (b) to find the total cost.

Total cost = 5k + 75s + 400

k = 2 and s = 5

= 5(2) + 75(5) + 400

= 10 + 375 + 400

= 785

Total cost = 785

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