Hanna shops for socks that cost $[tex]$2.99[/tex] for each pair and blouses that cost $[tex]$12.99[/tex] each. Let $[tex]$x$[/tex] represent the number of pairs of socks purchased, and let $[tex]$y$[/tex] represent the number of blouses purchased. Which equation models the purchases she made with $[tex]$43.92[/tex]?
A. $[tex]$x+y=15.98$[/tex]
B. $[tex]$x+y=43.92$[/tex]
C. $[tex]$43.92 x-2.99 y=12.99$[/tex]
D. $[tex]$2.99 x+12.99 y=43.92$[/tex]
Answer (2)
The cost of socks is 2.99 x .
The cost of blouses is 12.99 y .
The total cost is 2.99 x + 12.99 y .
The equation is 2.99 x + 12.99 y = 43.92 .
Explanation
Problem Analysis Let's analyze the problem. Hanna is buying socks and blouses. Each pair of socks costs $2.99 and each blouse costs $12.99 . We need to find the equation that represents the total amount she spent, which is $43.92 . Let x be the number of pairs of socks and y be the number of blouses.
Formulating the Equation The cost of x pairs of socks is 2.99 x . The cost of y blouses is 12.99 y . The total cost is the sum of these two, which must equal $43.92 . Therefore, the equation is: 2.99 x + 12.99 y = 43.92
Final Answer The equation that models the purchases Hanna made is 2.99 x + 12.99 y = 43.92 .
Examples
Imagine you're planning a school event and need to buy snacks and drinks. If each snack costs $2.99 and each drink costs $12.99 , and you have a budget of $43.92 , this equation helps you figure out how many snacks and drinks you can buy without exceeding your budget. This is a practical way to use algebra to manage expenses and make informed purchasing decisions.
The equation that models Hanna's purchases is 2.99 x + 12.99 y = 43.92 . This equation represents the total spending on socks and blouses. Therefore, the correct choice is option D.
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