Let's analyze each situation to determine which one cannot be modeled by the equation [tex]\(3x + 4y = 34\)[/tex].
Situation A:
3 kids' meals and 4 adult meals totaled to [tex]$34.
- Let \( x \) be the price of one kids' meal.
- Let \( y \) be the price of one adult meal.
- The equation \( 3x + 4y = 34 \) models this situation accurately, where \( 3 \) and \( 4 \) are the quantities of kids' meals and adult meals respectively, and \( 34 \) is the total cost.
Situation B:
A collection of $[/tex]3 baseball cards and [tex]$4 baseball cards is valued at $[/tex]34.
- Let [tex]\( x \)[/tex] be the number of [tex]$3 baseball cards.
- Let \( y \) be the number of $[/tex]4 baseball cards.
- The equation [tex]\( 3x + 4y = 34 \)[/tex] fits this situation, where [tex]\( 3 \)[/tex] and [tex]\( 4 \)[/tex] are the values of the baseball cards respectively, and [tex]\( 34 \)[/tex] is the total value.
Situation C:
A drawer contains 34 buttons, 3 of which are red and 4 of which are blue.
- This situation describes the total number of buttons as being [tex]\( 34 \)[/tex].
- If we tried to model this using the equation [tex]\( 3x + 4y = 34 \)[/tex], it would imply that there are quantities [tex]\( x \)[/tex] and [tex]\( y \)[/tex] such that [tex]\( 3x \)[/tex] represents the red buttons and [tex]\( 4y \)[/tex] represents the blue buttons.
- However, since the total number of buttons is not derived from a combination of multiples of [tex]\( 3 \)[/tex] and [tex]\( 4 \)[/tex], this equation does not logically fit this scenario.
Situation D:
Cindy worked as a restaurant greeter for 3 hours and as a cashier for 4 hours for a total earning of $34. Each job has a different rate of pay.
- Let [tex]\( x \)[/tex] be the hourly wage for the greeter position.
- Let [tex]\( y \)[/tex] be the hourly wage for the cashier position.
- The equation [tex]\( 3x + 4y = 34 \)[/tex] models this situation accurately, where [tex]\( 3 \)[/tex] and [tex]\( 4 \)[/tex] are the hours worked in each position respectively, and [tex]\( 34 \)[/tex] is the total earnings.
From the analysis, it is clear that:
Situation C cannot be modeled with the equation [tex]\(3x + 4y = 34\)[/tex].
