Suppose yogurt is on sale for $0.75 each, and you have a coupon for $0.50 off your total purchase. Write a function rule for the cost of x yogurts.

Number of yogurts: 1, 2, 3, 5, 7, x

Total cost: _ , _, _ ,_

1 answer

Let's break down the cost of purchasing \( x \) yogurts.

  1. Cost of Yogurts: Each yogurt costs $0.75, so the total cost for \( x \) yogurts without any coupon is given by: \[ \text{Cost of } x \text{ yogurts} = 0.75x \]

  2. Applying the Coupon: You have a coupon for $0.50 off the total purchase. Therefore, the total cost after applying the coupon is: \[ \text{Total cost with coupon} = 0.75x - 0.50 \]

Thus, the function rule for the cost of \( x \) yogurts, including the coupon discount, can be written as: \[ C(x) = 0.75x - 0.50 \]

Now, let's calculate the total costs for the specified values of \( x \):

  • For \( x = 1 \): \[ C(1) = 0.75(1) - 0.50 = 0.75 - 0.50 = 0.25 \]

  • For \( x = 2 \): \[ C(2) = 0.75(2) - 0.50 = 1.50 - 0.50 = 1.00 \]

  • For \( x = 3 \): \[ C(3) = 0.75(3) - 0.50 = 2.25 - 0.50 = 1.75 \]

  • For \( x = 5 \): \[ C(5) = 0.75(5) - 0.50 = 3.75 - 0.50 = 3.25 \]

  • For \( x = 7 \): \[ C(7) = 0.75(7) - 0.50 = 5.25 - 0.50 = 4.75 \]

Total Costs:

  • \( x = 1 \): $0.25
  • \( x = 2 \): $1.00
  • \( x = 3 \): $1.75
  • \( x = 5 \): $3.25
  • \( x = 7 \): $4.75

The total costs for the specified values of \( x \) are:

  • For 1 yogurt: $0.25
  • For 2 yogurts: $1.00
  • For 3 yogurts: $1.75
  • For 5 yogurts: $3.25
  • For 7 yogurts: $4.75