Question

2.
Bradley decides to include 5 pages of photographs for every 15 pages.
Use equivalent ratios to find how many pages of photographs will be in the
cookbook. Explain how you know the ratios are equivalent.

Answer 1

Certainly! Let's address this step-by-step:

1. Understand the given ratio:
- Bradley decides to include 5 pages of photographs for every 15 pages in the cookbook.

2. Establish the ratio:
- We can represent this ratio as 5 pages of photographs per 15 total pages. This can be written as the fraction $\(\frac{5}{15}\)$.

3. Simplify the ratio:
- Simplify $\(\frac{5}{15}\)$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
$\[ \frac{5 \div 5}{15 \div 5} = \frac{1}{3} \]$
- This simplified ratio ($\(\frac{1}{3}\)$) represents the proportion of pages that are photographs.

4. Interpret the ratio in words:
- The simplified ratio $\(\frac{1}{3}\)$ tells us that for every 3 pages in the cookbook, 1 page is a photograph.

5. Determine the total number of pages in the cookbook:
- Let's assume the cookbook has 60 pages in total.

6. Calculate the number of pages of photographs using the equivalent ratio:
- Since the simplified ratio is $\(\frac{1}{3}\)$, we know that one-third of all pages in the cookbook will be photographs.
- To find the number of pages of photographs, multiply the total number of pages by the ratio:
$\[ \frac{1}{3} \times 60 = 20 \]$

7. Conclusion:
- Therefore, if Bradley includes 5 pages of photographs for every 15 pages in the cookbook, there will be 20 pages of photographs in a 60-page cookbook.

So, the ratio of 5 pages of photographs for every 15 pages is equivalent to having 20 pages of photographs in a cookbook with 60 total pages.