Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker ne
eds to pass two checkpoints before completing a race. The total distance for the race is 120 miles. The distance from the starting point to checkpoint 1 is 35 miles more than half the distance from checkpoint 1 to checkpoint 2. The distance from checkpoint 2 to the finish line is 20 miles less than twice the distance from checkpoint 1 to checkpoint 2. Let x represent the distance from the starting point to checkpoint 1, y represent the distance from checkpoint 1 to checkpoint 2, and z represent the distance from checkpoint 2 to the finish line. Complete the matrix equation that models this situation, A-1B = X.
2 answers:
Answer:
The matrix equation is
Step-by-step explanation:
* Lets change the story problem to equations
- The distance between the starting point and checkpoint 1 is x
- The distance between checkpoint 1 to checkpoint 2 is y
- The distance between checkpoint and the finish line is z
- The total distance for the race is 120 miles
∴ x + y + z = 120 ⇒ (1)
-The distance from the starting point to checkpoint 1 is 35 miles
more than half the distance from checkpoint 1 to checkpoint 2
∵ The distance from the starting point to checkpoint 1 is x
∵ The distance from checkpoint 1 to checkpoint 2 is y
- x is more than half y by 35
∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides
∴ x - (1/2) y = 35 ⇒ (2)
- The distance from checkpoint 2 to the finish line is 20 miles less
than twice the distance from checkpoint 1 to checkpoint 2
∵ The distance from checkpoint 2 to the finish line is z
∵ the distance from checkpoint 1 to checkpoint 2 is y
- z is less than twice y by 20
∴ z = 2y - 20 ⇒ add 20 to both sides
∴ z + 20 = 2y ⇒ subtract z from both sides
∴ 2y - z = 20 ⇒ (3)
* Now lets write the three equations
# x + y + z = 120 ⇒ (1)
# x - (1/2) y = 35 ⇒ (2)
# 2y - z = 20 ⇒ (3)
- Now lets write the matrix equation that models this situation
∴
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