Jackie runs and dances for a total of 55 minutes every day. She dances 25 minutes more than she runs.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day.

Part B: How much time does Jackie spend running every day?

Part C: Is it possible for Jackie to have spent 45 minutes dancing every day? Explain your reasoning.

Part A: The pair of linear equations is

x + y = 55

y = x + 25

Part B: Jackie spends 15 minutes running every day

Part C: It is impossible for Jackie to have spent 45 minutes dancing if she runs and dances for a total of exactly 55  minutes and dances for 25 minutes longer than she runs

Step-by-step explanation:

The given:

Jackie runs and dances for a total of 55 minutes every day

She dances for 25 minutes longer than she runs

Jackie runs for x minutes

She dances for y minutes every day

∵ Jackie runs and dances for a total of 55 minutes every day

∵ Jackie runs for x minutes and dance for y minutes every day

- Add x and y, then equate the sum by 55

∴ x + y = 55 ⇒ (1)

∵ She dances for 25 minutes longer than she runs

- Equate y by the sum of x and 25

∴ y = x + 25 ⇒ (2)

Part A: The pair of linear equations is

x + y = 55

y = x + 25

Let us solve the system of equations

Substitute y in equation (1) by equation (2)

∴ x + x + 25 = 55

- Add the like terms in the left hand side

∴ 2 x + 25 = 55

- Subtract 25 from both sides

∴ 2 x = 30

- Divide both sides by 2

∴ x = 15

Part B: Jackie spends 15 minutes running every day

Substitute the value of x in equation (20 to find y

∵ y = 15 + 25

∴ y = 40

∴ Jackie spends 40 minutes dancing every day

Jackie can not dance for 45 minutes if she runs and dances for a total of exactly 55  minutes and dances for 25 minutes longer than she runs because 45 - 25 = 20 so she runs for 20 minutes and 45 + 20 = 65 minutes not 55

∴ it is impossible

Part C: It is impossible for Jackie to have spent 45 minutes dancing if she runs and dances for a total of exactly 55  minutes and dances for 25 minutes longer than she runs

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answer:

Part A: Write a pair of linear equations to show the relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day.

Step-by-step explanation:

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step-by-step explanation:

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

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