## Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker needs to pass

Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker needs 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.

## Answers ( )

These are the options: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

∴