Question

maple grove wants to include two types of maple trees, the namesake of the city, for their parks. two varieties of maple trees have been selected. one variety costs $75 per tree; the other more colorful variety costs $85 per tree. the tree budget must not exceed $56,000. citizens want more of the colorful $85 trees than the others if possible.
let x be the number of $75 trees and y the number of $85 trees. which system of inequalities represents this situation?
click on the correct answer.
$75x + 85y \geq 56,000$ $x \geq y$
$75x + 85y \leq 56,000$ $x \geq y$
$75x + 85y \leq 56,000$ $x \leq y$
$75x + 85y \geq 56,000$ $x \leq y$

Explanation:

Step1: Analyze the cost inequality

The total cost of \( x \) $75 trees and LXI1 $85 trees is \( 75x + 85y \). The budget must not exceed $56,000, so \( 75x + 85y \leq 56000 \).

Step2: Analyze the quantity inequality

Citizens want more of the $85 (colorful) trees, so the number of $75 trees (\( x \)) should be less than or equal to the number of $85 trees (\( y \)), i.e., \( x \leq y \).

Answer:

75x + 85y ≤ 56,000
x ≤ y