Question

Ya idk how to do this plz help explain if you can

Answer 1

Answer:

  92 attendees had activity cards

Step-by-step explanation:

Let x be the number of students with activity cards. Then 130-x is the number without, and the total revenue is ...

  7x +10(130 -x) = 1024

  7x +1300 -10x = 1024 . . . . eliminate parentheses

  -3x = -276 . . . . . . . . . . . . . collect terms; subtract 1300

  x = 92 . . . . . . divide by 3

92 students with activity cards attended the dance.

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Comment on the solution

Often, you will see such a problem solved using two equations. For example, they might be ...

Let 'a' represent the number with an activity card; 'w' the number without. Then ...

• a+w = 130 . . . . the total number of students
• 7a +10w = 1024 . . . . the revenue from ticket sales

The problem statement asks for the value of 'a', so you want to eliminate w from these equations. You can do that using substitution. Using the first equation to write an expression for w, you have ...

  w = 130-a

and making the substitution into the second equation gives ...

  7a +10(130 -a) = 1024

This should look a lot like the equation we used above. There, we skipped the extra variable and went straight to the single equation we needed to solve.