Question

use the scenarios and elimination by addition or subtraction to answer the questions.
4.8) two times a number minus four times another number is ten, and four times the first number minus four times the second number results in four. what are the two numbers? let the first number be x and the second number be y.
4.9) 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.
standardized assessment practice
choose the correct answer.
4.10) 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.
a. $10.00
b. $10.05
c. $9.05
d. $9.50

Explanation:

Step1: Set up equations for 4.8

Based on the problem, we have the system of equations:
$2x - 4y=10$ and $4x - y = 4$. Multiply the first - equation by 2 to get $4x-8y = 20$.

Step2: Subtract equations

Subtract the new - formed equation from the second equation: $(4x - y)-(4x - 8y)=4 - 20$.
Simplify: $4x - y-4x + 8y=-16$, which gives $7y=-16$, so $y =-\frac{16}{7}$.
Substitute $y =-\frac{16}{7}$ into $4x - y = 4$, we get $4x+\frac{16}{7}=4$, $4x=4-\frac{16}{7}=\frac{28 - 16}{7}=\frac{12}{7}$, $x=\frac{3}{7}$.

Step3: Set up equations for 4.9

We have the system of equations: $x - y = 6$ and $x + y = 34$.
Add the two equations: $(x - y)+(x + y)=6 + 34$.
Simplify: $2x=40$, so $x = 20$.
Substitute $x = 20$ into $x + y = 34$, we get $20 + y = 34$, $y = 14$.

Step4: Set up equations for 4.10

We have the system of equations: $2x+3y = 72.85$ and $2x + 5y=94.75$.
Subtract the first equation from the second equation: $(2x + 5y)-(2x + 3y)=94.75 - 72.85$.
Simplify: $2y=21.9$, so $y = 10.95$.
Substitute $y = 10.95$ into $2x+3y = 72.85$, $2x+3\times10.95 = 72.85$, $2x+32.85 = 72.85$, $2x=40$, $x = 20$.
The difference between the cost of an adult ticket and a kid ticket is $x - y=20 - 10.95 = 9.05$.

Answer:

4.8: $x=\frac{3}{7},y =-\frac{16}{7}$
4.9: $x = 20,y = 14$
4.10: C. $9.05$