Question

1. use the scenario and elimination by addition or subtraction to answer the question. the difference between the length and width of a rectangle is 6, and their sum is 34. what are the length and width of the rectangle? let the length be x and the width be y. the length of the rectangle is 20 and the width is 14. the length of the rectangle is 18 and the width is 14. the length of the rectangle is 14 and the width is 18. the length of the rectangle is 24 and the width is 10. 10) standardized assessment practice choose the correct answer. heathers family has 2 adults and 3 kids. the tickets to the musical cost them $72.85. carls family, on the other hand, paid $94.75 for 2 adults and 5 kids. how much higher was the cost of an adults ticket compared to a kids ticket? let the cost of an adults ticket be x and the cost of a kids ticket be y. $10.00 $9.05 $9.50 $10.05

Explanation:

Step1: Set up equations for rectangle problem

We have the system of equations: $x - y=6$ and $x + y=34$.

Step2: Add the two equations

Adding the two - equations $(x - y)+(x + y)=6 + 34$. Simplifying gives $2x=40$, so $x = 20$.

Step3: Find the value of y

Substitute $x = 20$ into $x + y=34$, we get $20+y=34$, then $y=34 - 20=14$.

Step4: Set up equations for ticket - price problem

For Heather's family: $2x+3y = 72.85$. For Carl's family: $2x+5y = 94.75$.

Step5: Subtract the first ticket - price equation from the second

$(2x + 5y)-(2x+3y)=94.75 - 72.85$. Simplifying gives $2y=21.9$, so $y = 10.95$.

Step6: Find the value of x

Substitute $y = 10.95$ into $2x+3y = 72.85$, we have $2x+3\times10.95=72.85$. Then $2x+32.85 = 72.85$, $2x=72.85 - 32.85=40$, and $x = 20$.

Step7: Calculate the difference between adult and kid ticket prices

$x-y=20 - 10.95=9.05$.

Answer:

1. The length of the rectangle is 20 and the width is 14.
2. $9.05$