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Question

Which situation could the equation 1.5x+8=12.5
represent?(1 point)
Responses

Toby spent $12.50 at the amusement park. He went on x rides for $8 each, and he also bought a drink for $1.50.
Toby spent $12.50 at the amusement park. He went on x rides for $8 each, and he also bought a drink for $1.50.

Samantha bought x bottles of juice for $1.50 each. She used an $8 gift card. The total amount she had to pay was $12.50.
Samantha bought x bottles of juice for $1.50 each. She used an $8 gift card. The total amount she had to pay was $12.50.

Jazmin bought a pizza for $12.50. A plain cheese pizza is $8. She got x additional toppings, which cost $1.50 each.
Jazmin bought a pizza for $12.50. A plain cheese pizza is $8. She got x additional toppings, which cost $1.50 each.

Michael wants to earn $12.50 to buy a book. He earns $8 each time he walks the neighbor’s dog, which he has done x times. He still needs to earn $1.50.

1 answer

To determine which situation the equation \( 1.5x + 8 = 12.5 \) represents, let's break down the components of the equation:

  • The term \( 1.5x \) suggests that a cost is being calculated based on a quantity \( x \) multiplied by $1.50. This could represent the cost of buying \( x \) items, each costing $1.50.
  • The term \( + 8 \) suggests that there is a fixed cost of $8 being added to the cost based on \( x \).
  • The equation equals \( 12.5 \), indicating that the total cost of the fixed amount ($8) plus the variable amount ($1.50 per item) equals $12.50.

Now let's evaluate the provided responses:

  1. Toby's situation: He spent $12.50, went on \( x \) rides for $8 each, and bought a drink for $1.50. This would imply that the equation doesn't match because expenses don't align.

  2. Samantha's situation: She bought \( x \) bottles of juice for $1.50 each and used an $8 gift card. The total amount to pay would be $1.50x - 8 = 12.50, which doesn't fit our equation.

  3. Jazmin's situation: She bought a pizza for $12.50, with a base cost of $8 and \( x \) additional toppings at $1.50 each. This can be interpreted as \( 8 + 1.5x = 12.5 \), which matches our equation rearranged.

  4. Michael's situation: To earn $12.50, making $8 each time he walks the dog, there's a different arrangement of earnings that wouldn't fit this equation as well.

Based on the analysis, the situation that \( 1.5x + 8 = 12.5 \) represents is:

Jazmin bought a pizza for $12.50. A plain cheese pizza is $8. She got \( x \) additional toppings, which cost $1.50 each.