Question

Lydia was comparing the price of grapefruit juice at two stores. The equation y = 1.7x represents what Lydia would pay in dollars and cents, y, for x bottles of grapefruit juice at store B. Lydia can buy 7 bottles of grapefruit juice at Store A for a total cost of $12.60. How much less is a bottle of grapefruit juice at Store B than at Store A?

Answer 1

To determine how much less a bottle of grapefruit juice costs at Store B compared to Store A, we calculate the cost per bottle at Store A to be $1.80 and use the given equation y = 1.7x to find that the cost per bottle at Store B is $1.70. Thus, Store B is $0.10 less expensive per bottle.

Step-by-step explanation:

To find out how much less a bottle of grapefruit juice costs at Store B compared to Store A, we first need to determine the cost per bottle at Store A. Since Lydia can buy 7 bottles for $12.60 at Store A, we divide the total cost by the number of bottles to get the cost per bottle:

Cost per bottle at Store A = Total cost at Store A / Number of bottles

Cost per bottle at Store A = $12.60 / 7 bottles

Cost per bottle at Store A = $1.80

Now, using the equation y = 1.7x for Store B, where y represents the total cost and x the number of bottles, we calculate the cost per bottle at Store B:

Since x represents 1 bottle, we can see that y = 1.7 × 1 which means the cost per bottle at Store B is $1.70.

To find the difference in cost per bottle between the two stores, we subtract the cost per bottle at Store B from the cost per bottle at Store A:

Difference in cost = Cost per bottle at Store A - Cost per bottle at Store B

Difference in cost = $1.80 - $1.70

Difference in cost = $0.10

So, a bottle of grapefruit juice is $0.10 less at Store B than at Store A.