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As part of a landscaping project, Mr. Ortega is purchasing plants from a garden center. It will cost $\$34$ to buy a mature tree, versus $\$8$ for a young one. His target is to keep the cost under $\$820$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of mature trees $\newline$ $y =$ the number of young trees $\newline$ Choices: $\newline$ (A) $34x + 8y < 820$ $\newline$ (B) $34x - 8y > 820$ $\newline$ (C) $34x + 8y > 820$ $\newline$ (D) $34x + 8y < 820$

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Write two-variable inequalities: word problems

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Q. As part of a landscaping project, Mr. Ortega is purchasing plants from a garden center. It will cost

\$34

to buy a mature tree, versus

\$8

for a young one. His target is to keep the cost under

\$820

.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mature trees

\newline

y =

the number of young trees

\newline

Choices:

\newline

(A)

34x + 8y < 820

\newline

(B)

34x - 8y > 820

\newline

(C)

34x + 8y > 820

\newline

(D)

34x + 8y < 820

Calculate Mature Tree Cost: Determine the cost for purchasing mature trees. The cost of one mature tree is $\$34$ , and if Mr. Ortega buys $x$ mature trees, the total cost for mature trees will be $34x$ .
Calculate Young Tree Cost: Determine the cost for purchasing young trees. The cost of one young tree is $\$8$ , and if Mr. Ortega buys $y$ young trees, the total cost for young trees will be $8y$ .
Combine Total Cost: Combine the costs for mature and young trees to represent the total cost. The total cost for both mature and young trees is the sum of the cost for mature trees and the cost for young trees, which is $34x + 8y$ .
Set Cost Limit: Mr. Ortega wants to keep the total cost under $\$820$ . This means the combined cost of mature and young trees must be less than $\$820$ . Therefore, the inequality that represents this situation is $34x + 8y < 820$ .

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