Final answer:
Equations are established to represent real-world relationships. Solving for the unknown variable 'n' provides answers to the problems: Allan has 103 baseball cards, Michelle jogs at 4 mph, r equals 0.5, z equals 0, and n equals 1.
Step-by-step explanation:
Practice Test 4 Solutions: Linear Equations
For the given problems, we will establish linear equations and solve them.
Problem 16)
Allan has 84 baseball cards which is 19 fewer than Mike. To represent this situation using the variable -n we write the equation:
n = 84 + 19. Solving this, we find that Mike has n = 103 baseball cards.
Problem 17)
Jamie can ride her bike 3 times as fast as Michelle can jog. If Jamie rides at 12 miles per hour, the equation to find Michelle's jogging speed is:
n = 12 / 3. Solving this, Michelle jogs at 4 miles per hour.
Problem 18)
For the equation 5 + r = 6 - r, we solve for r by adding r to both sides and subtracting 5 from both sides:
2r = 1. Dividing both sides by 2 gives us r = 0.5.
Problem 19)
The equation z - 16 = -16 simply tells us that z is 0 since adding 16 to both sides cancels out the 16 and leaves us with z = 0.
Problem 20)
To solve 7n - 7 = 0, we add 7 to both sides to isolate the term with n:
7n = 7. Dividing both sides by 7 gives us n = 1.
It is important to always check the reasonableness of your answer after solving.