My little cousin asked me to help her with her Alg 2 homework because she knew that in high school I had either honors or AP math every year.
But I don't remember any of what she's asking me, except for matrices, and I feel so bad, seeing as she's been sick and hasn't learned this and was counting on me. So could anyone help out?
-A school held a basketball game.
An adult ticket is $3, a student ticket is $1.
292 tickets were sold. In total, the school made $470.
Write an solve a system to the amount of each kind of ticket.
-Which expression can be used to substitute for y in the first equation of this system?
5x-2y=8
x-y=1
A) x - 1
B) x + 1
C) 1 - x
D) 1 + x
and finally,
-Krista works for $5/hour at the video store and $7/hour landscaping. She has to work at least 4 hours a week at the video store but she can't work more than 15 hours a week, total. Write out an expression the the maximum she can earn in a week. Define the variables and answer what the constraints are. Give coordinates as if you were to graph this.
Could you please help?
Thank you! :)
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Answers & Comments
Verified answer
-First question:
Let x be the number of adult tickets and y the number of child tickets.
The total number of tickets is 292, so x + y = 292
She makes 3x dollars from the adult tickets, and y from the child tickets. She makes 470 dollars in total so 3x + y = 470.
So you have the simultaneous equations
x+y = 292
3x + y = 470
From the first equation, y = 292 - x. Substitute into the second equation.
3x + 292 - x = 470
2x = 178
x = 89
y = 292 - x = 292 - 89 = 203.
So she sells 89 adult tickets and 203 child tickets.
-Second question:
x - y = 1. Subtracting x from both sides:
-y =1 - x. Multiply by -1 to get
y = x - 1, so the answer is A).
-Third question
Since she must work at least 4 hrs in the video store and no more than 15 in total, she must spend no more than 11 hours landscaping. Defining the variables, let x be the number of hours working in the video story and y be the number of hours landscaping. Constraints are x≥4 and y≤11. She will earn 5x + 7y. Maximum she will earn is when x = 4 and y = 11, and she will earn 4*5 + 11*7 = 97 dollars.