Question

PLEASE help!!!! 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. (5 points) Part B: How much time does Jackie spend running every day? (3 points) Part C: Is it possible for Jackie to have spent 45 minutes dancing every day? Explain your reasoning

Answer 1

Part a:

x + y = 55

y = x + 25

part b:

jackie runs 15 minutes every day.

part c:

it is not possible for jackie to spend 45 minutes a day dancing, since the time she spends dancing and running is 55 minutes, and we know that it takes 15 minutes to run

step-by-step explanation:

let's call and while jackie is dancing

let's call x while jackie is running

then we know that jackie runs and dances for a total of 55 minutes every day

this means that:

x + y = 55

we also know that jackie dances 25 minutes more than she runs.

this meant that:

y = x + 25

now we substitute the second equation in the first and solve for the variable x

x + x + 25 = 552x = 55-252x = 30x = 15

jackie runs 15 minutes every day.

now we find the value of the variable -y

15 + y = 55y = 55-15y = 40

note that it is not possible for jackie to spend 45 minutes a day dancing, since the time she spends dancing and running is 55 minutes, and we know that it takes 15 minutes to run

Answer 2

for this case we have:

x: variable that represents the number of minutes jackie runs.

y: variable that represents the number of minutes jackie dances.

according to the data we have:

x + y = 55\\25 + x = y

to solve the system, we substitute the second equation in the first one:

x + 25 + x = 55\\2x = 55-25\\2x = 30\\x = \frac {30} {2}\\x = 15

so, jackie runs 15 minutes a day.

y = 25 + x\\y = 25 + 15\\y = 40

so, jackie dances 40 minutes a day.

it is not possible that jackie has spent 45 minutes dancing in one day. since he dedicates 55 minutes to both activities, he runs 15 minutes and the rest dances.

part a:

x + y = 55\\25 + x = y

part b:

jackie runs 15 minutes per day.

part c:

it's not possible.