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

Answer 1

Answer: A. x + y = 75 B. She spends 25 minutes running and 50 minutes dancing every day. C. Yes it is.

Step-by-step explanation: B. She spends 25 minutes running and 50 minutes dancing every day, because if she dances for 25 more minutes then she runs then we can minus 25 from 75 which we get 50. Then we take the 50 a divide it by 2 because of the two categories dancing and running. So we know she spends 25 minutes running then 25 minutes dancing but we need to add the 25 minutes to dancing. So she spends 25 minutes running and 50 dancing. C. Yes it is because she already dances for 50 minutes a day so all she needs to do is workout for 10 minutes less so 65 minutes one day.

Answer 2

A system of linear equation consists of multiple linear equations

• The system of linear equations is: $\mathbf{x + y = 75}$ and $\mathbf{y = 25 + x}$
• She spends 25 minutes running
• It is possible to dance 45 minutes every day

(a) A pair of linear equations

She dances and runs for 75 minutes.

So:

$\mathbf{x + y = 75}$

She dances 25 minutes more than she runs.

So:

$\mathbf{y = 25 + x}$

So, the system of linear equations is: $\mathbf{x + y = 75}$ and $\mathbf{y = 25 + x}$

(b) The time she spends running every day

Substitute 25 + x for y in $\mathbf{x + y = 75}$

$\mathbf{x + 25 + x = 75}$

Subtract 25 from both sides

$\mathbf{2x = 50}$

Divide both sides by 2

$\mathbf{x = 25}$

Hence, she spends 25 minutes running

(c) Is it possible to dance 45 minutes each day

We have:

$\mathbf{y = 25 + x}$

So:

$\mathbf{y = 25 + 45}$

$\mathbf{y = 70}$

This means that, she has to spend less minute running and dancing.

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