Ask a New Question
Menu

Each equation below is followed by several stories.

Select all of the stories that can be represented by the equation.
If none of the stories can be represented, select "None of the above".
(a) 50х - 25 = 675
(b) 24x + 36 = 156

A fitness center charges x dollars for each personal training hour. Last year, Brian received a one-time, new
• member discount of $25. He used 50 personal training hours last year. He paid a total of $675 after the discount.

A fitness center charges $25 for each personal training o hour. Last year, Brian received a one-time, new member discount of $50. Brian used r personal training hours last year. He paid a total of $675 after the discount.

A fitness center charges x dollars for each personal training hour. Last year, Brian received a one-time, new O member discount of $50. Brian used 25 personal training hours last year. He paid a total of $675 after the discount.

A fitness center charges $50 for each personal training hour. Last year, Brian received a one-time, new member discount of $25. Brian used r personal training hours last year. He paid a total of $675 after the discount.

• None of the above

Today, Rachel used $36 of her savings to buy a bike. She has been putting $24 into her savings each week for x weeks. After buying the bike, she now has $156 left in her savings.

Rachel is saving money and already has $36 saved. She is going to save an additional x dollars each week for 24 weeks. This will give her enough money for a bike that costs $156.

Rachel is saving money and already has $36 saved. She is going to save an additional $24 each week for x weeks. This will give her enough money for a bike that costs $156.

Today, Rachel used $36 of her savings to buy a bike. She has been putting x dollars into her savings each week for 24 weeks. After buying the bike, she now has $156 left in her savings.

• None of the above

1 answer

Let's analyze each equation and the corresponding stories.

(a) 50x - 25 = 675 This equation can be broken down as follows:

  • The fitness center charges \(x\) dollars per training hour.
  • The new member discount is $25.
  • After using 50 personal training hours, the total cost before the discount is \(50x\).
  • After the discount of $25, the total amount paid is $675.

Now, let's evaluate the stories:

  1. Story 1: A fitness center charges \(x\) dollars for each personal training hour. Last year, Brian received a one-time, new member discount of $25. He used 50 personal training hours last year. He paid a total of $675 after the discount.

    • This matches the equation. (Valid)

  2. Story 2: A fitness center charges $25 for each personal training hour. Last year, Brian received a one-time, new member discount of $50. Brian used \(r\) personal training hours last year. He paid a total of $675 after the discount.

    • Here, the charge is fixed at $25, not \(x\) based on the equation. (Invalid)

  3. Story 3: A fitness center charges \(x\) dollars for each personal training hour. Last year, Brian received a one-time, new member discount of $50. Brian used 25 personal training hours last year. He paid a total of $675 after the discount.

    • The hours used (25) does not match the 50 required in the equation. (Invalid)

  4. Story 4: A fitness center charges $50 for each personal training hour. Last year, Brian received a one-time, new member discount of $25. Brian used \(r\) personal training hours last year. He paid a total of $675 after the discount.

    • This does not utilize a variable \(x\) but rather specifies the charge as $50 directly. (Invalid)

Valid story for (a): Story 1.

(b) 24x + 36 = 156 This equation can be interpreted as:

  • Rachel has $36 saved.
  • She saves $24 each week for \(x\) weeks.
  • After saving, she has $156.

Now, let's evaluate the stories:

  1. Story 1: Today, Rachel used $36 of her savings to buy a bike. She has been putting $24 into her savings each week for \(x\) weeks. After buying the bike, she now has $156 left in her savings.

    • The story reflects that after saving and spending $36 she is left with $156. This aligns with the equation. (Valid)

  2. Story 2: Rachel is saving money and already has $36 saved. She is going to save an additional \(x\) dollars each week for 24 weeks. This will give her enough money for a bike that costs $156.

    • This suggests saving \(x\) per week over 24 weeks, which does not match the equation. (Invalid)

  3. Story 3: Rachel is saving money and already has $36 saved. She is going to save an additional $24 each week for \(x\) weeks. This will give her enough money for a bike that costs $156.

    • This does not match as saving for \(x\) weeks is incorrect based on the equation. (Invalid)

  4. Story 4: Today, Rachel used $36 of her savings to buy a bike. She has been putting \(x\) dollars into her savings each week for 24 weeks. After buying the bike, she now has $156 left in her savings.

    • The variable is incorrectly applied. It should be a constant $24 per week, not \(x\). (Invalid)

Valid story for (b): Story 1.

Final Selections:

  • For (a), the valid story is: Story 1.
  • For (b), the valid story is: Story 1.