Lamonte was comparing the price of grapefruit juice at two stores. The equation y, equals, 1, point, 7, 5, xy=1.75x represents what Lamonte would pay in dollars and cents, yy, for xx bottles of grapefruit juice at store A. Lamonte can buy 17 bottles of grapefruit juice at Store B for a total cost of $36.38.

Question

How much less is a bottle of grapefruit juice at Store A than at Store B?

Answer 1

To find out how much less a bottle of grapefruit juice at Store A costs compared to Store B, we first need to determine the cost per bottle at Store B and then find the cost per bottle at Store A using the given equation.

1. Calculate the cost per bottle at Store B:

   Lamonte buys 17 bottles of grapefruit juice at Store B for a total cost of $36.38.

   The cost per bottle at Store B can be calculated as: \[ \text{Cost per bottle at Store B} = \frac{\text{Total cost at Store B}}{\text{Number of bottles}} = \frac{36.38}{17} \]

   \[ \frac{36.38}{17} = 2.141176 \]

   Rounding to the nearest cent: \[ \text{Cost per bottle at Store B} \approx 2.14 \]

2. Calculate the cost per bottle at Store A:

   The equation provided for the cost at Store A is \( y = 1.75x \).

   If we let \( x = 1 \) (representing one bottle at Store A): \[ y = 1.75(1) = 1.75 \]

   Thus, the cost per bottle at Store A is: \[ \text{Cost per bottle at Store A} = 1.75 \]

3. Determine the price difference:

   Now we can find out how much less a bottle of grapefruit juice at Store A costs compared to Store B: \[ \text{Difference} = \text{Cost per bottle at Store B} - \text{Cost per bottle at Store A} \] \[ \text{Difference} = 2.14 - 1.75 = 0.39 \]

Therefore, the cost of a bottle of grapefruit juice at Store A is $0.39 less than at Store B.