Question

Jackie runs and dances for 75 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
runs (x) and the number of minutes she dances (y) every day.

Part B: How much time does Jackie spend running every day? Show your work.

Part C: What is the greatest amount of time she could spend dancing every day, given she will take a
run.

Explain your reasoning.

PLEASE HELP DUE SOON!

Answer 1

A. y = x + 25

x + y = 75

B. 25 minutes

C. 50 minutes

Explanation:

Define the variables:

• Let x = the number of minutes Jackie runs every day.
• Let y = the number of minutes Jackie dances every day.

Part A

If Jackie dances 25 minutes more than she runs:

`\implies y=x+25`

If Jackie runs and dances for 75 minutes:

`\implies x+y=75`

Part B

Substitute the first equation into the second equation and solve for x:

`\implies x+(x+25)=75`

`\implies 2x+25=75`

`\implies 2x+25-25=75-25`

`\implies 2x=50`

`\implies 2x/ 2=50 / 2`

`\implies x=25`

Therefore, Jackie spends 25 minutes running everyday.

Part C

Substitute the found value of x into the first equation and solve for y:

`\implies y=25+25`

`\implies y=50`

Therefore, the greatest amount of time Jackie could spend dancing every day, given she will take a run, is 50 minutes.