Question

question 1-17
sanjay buys ( x ) boxes of hot wings and ( y ) bottles of soda for a party. the numbers of boxes of hot wings and bottles of soda he can buy with $40 can be represented with the inequality shown
( 40 geq 6x + 2y )

Explanation:

Step1: Identify the problem type

This is a linear inequality problem related to real - life budgeting (Sanjay's money for buying hot wings and soda), which falls under the subfield of Algebra (in Mathematics) as it involves linear expressions and inequalities with variables \(x\) and \(y\).

Step2: Analyze the inequality

The inequality \(40\geq6x + 2y\) represents the total cost of \(x\) boxes of hot wings (where each box costs \(\$6\), so the cost for hot wings is \(6x\)) and \(y\) bottles of soda (where each bottle costs \(\$2\), so the cost for soda is \(2y\)) being less than or equal to \(\$40\) (the total money Sanjay has). If we were to find the possible values of \(x\) and \(y\), we could use methods like finding the intercepts (when \(x = 0\), \(40\geq2y\Rightarrow y\leq20\); when \(y = 0\), \(40\geq6x\Rightarrow x\leq\frac{40}{6}=\frac{20}{3}\approx6.67\)) or graphing the inequality (the region below or on the line \(6x + 2y=40\) (or \(3x + y = 20\)) in the first quadrant since \(x\) and \(y\) represent the number of items and can't be negative).

Answer:

This problem is in the subfield of Algebra (Mathematics) and is represented by the linear inequality \(40\geq6x + 2y\) which models the cost constraint for buying hot wings (\(x\) boxes at \(\$6\) each) and soda (\(y\) bottles at \(\$2\) each) with \(\$40\).