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Let x be the food costs and y the clothing costsfor the year. Which system of inequalitiesrepresents their budget?Click on the correct answer.Kay and Jerry have a yearly householdbudget for food and clothing that mustnot exceed $5200. Their food costincludes going out to dinner one nighteach weekend, or 52 times a year, andspending an average of $20 or less. Foodcost also includes $70 or less per weekfor groceries.x 70x + y s 5200XS 4860x + y s 5200XS 3640x + y s 52002x 290x + y s 5200



Answer :

Kay and Jerry have a yearly household budget for food and clothing that must not exceed $5200

Thus, we must have that

[tex]\begin{gathered} \text{ the sum of the food cost and the clothing cost for the year must be less than or} \\ \text{ \$5200} \end{gathered}[/tex]

This means that

[tex]x+y\le5200[/tex]

Their food cost includes going out to dinner one night each weekend, or 52 times a year, and spending an average of $20 or less. Food cost also includes $70 or less per week for groceries.

Hence,

[tex]\begin{gathered} x\le(52\times20)+(52\times70) \\ \text{ thus} \\ x\le1040+3640 \\ x\le4680 \end{gathered}[/tex]

Hence, the system of inequalities that represents their budget is given by

x ≤ 4680, x + y ≤ 5200