Question

Part A: During a sidewalk sale, a bookstore charges a rate that varies directly with the number of books bought. Georgia spent $62.82 when she bought 9 books during Complete the multiplication equation to find the total cost of any number of books. Let t represent the total cost, and let b represent the number of books bought. t= Part B: William bought 4 books. Using the equation you wrote in part A, how much did William spend on books? Round your answer to the nearest hundredth.​

Answer 1

To find the total cost of any number of books, we can set up a proportion using the given information. Using the equation t/b = $62.82/9, we can find the total cost for any number of books b. For Part B, we plug in the value of b into the equation to find the cost for 4 books.

Step-by-step explanation:

To find the total cost of any number of books, we can set up a proportion using the information given. We know that the rate varies directly with the number of books bought. Let's set up the equation: t/b = $62.82/9. Now, we can write the equation using variables t and b: t/b = 62.82/9. To find the total cost t, we can cross multiply and solve for t. Cross multiplying gives us tb = 9 * 62.82. So, the equation is tb = 565.38.

For Part B, we are given that William bought 4 books. We can use the equation we found in Part A: tb = 565.38. Substituting b = 4 into the equation gives us t * 4 = 565.38. Solving for t, we divide both sides of the equation by 4. t = 565.38 / 4. Evaluating this expression gives us t = 141.34.

Answer 2

The total cost of books varies directly with the number bought, represented by the equation t = $6.98 × b. Using this, we calculate that William, who bought 4 books, spent $27.92.

Step-by-step explanation:

Part A: Finding the Total Cost of Books

To find the total cost of any number of books, we need to establish a linear equation that relates the total cost to the number of books bought. Since the cost varies directly with the number of books, we can write the equation in the form t = kb, where t represents the total cost, b represents the number of books bought, and k is the constant of proportionality (the cost per book). To find k, we use the information that Georgia spent $62.82 for 9 books:

k = total cost / number of books = $62.82 / 9 books

Calculating this, we get:

k = $6.98 per book

So, the equation to find the total cost for any number of books is:

t = $6.98 × b

Part B: Calculating William's Total Cost

Now that we have our equation, we can calculate the cost for William, who bought 4 books:

t = $6.98 × 4

t = $27.92

Therefore, William spent $27.92 on books.