The equation to find the price P for N number of bookmarks, plus the price of the gift box, is:
P = (N/7) * 3.50 for N < 10
P = (N/10) * 4.70 for N >= 10
Step-by-step explanation:
We are given two different prices for sets of bookmarks, one containing 7 bookmarks and the other containing 10 bookmarks. We want to find a general equation that will allow us to calculate the price P for any number of bookmarks N, along with the price of the gift box.
To do this, we can use the concept of proportionality. We know that the price of the gift box is the same for both sets of bookmarks, so we only need to consider the cost of the bookmarks themselves. We can set up a proportion between the number of bookmarks and the cost of the set:
7 bookmarks costs $3.50
10 bookmarks costs $4.70
We can simplify this proportion by dividing both sides by the number of bookmarks:
1 bookmark costs $0.50 (from 7 bookmarks for $3.50)
1 bookmark costs $0.47 (from 10 bookmarks for $4.70)
Now we have the cost per bookmark for each set. To find the total cost of N bookmarks, we can multiply the cost per bookmark by the number of bookmarks:
P = (N/7) * 3.50 for N < 10
P = (N/10) * 4.70 for N >= 10
We have to use a different equation depending on whether N is less than 10 or greater than or equal to 10, since we are dealing with two different sets of bookmarks. We also need to add the cost of the gift box to get the total price.