Final answer:
To find the equivalent ratio of 21:28 to _:24, simplify the original ratio to 3:4, identify the multiplication factor to reach 24 from 4, which is 6, and then multiply the corresponding part of the simplified ratio (3) by the same factor to get 18. Therefore, the equivalent ratio is 21:28 = 18:24.
Step-by-step explanation:
To solve the problem and fill in the blank to make an equivalent ratio 21: 28 = _: 24, we need to find a number that when paired with 24 forms the same ratio as 21 to 28. We will use cross-multiplication to solve for the missing value.
The original ratio can be simplified by dividing both terms by 7, which gives us 3: 4, indicating that the ratio represents a multiple of 3 to a multiple of 4. If we recognize 24 as 4 multiplied by 6, then to preserve the ratio, the missing number should be 3 multiplied by the same factor (6), resulting in 18. So, 21: 28 = 18: 24 is the equivalent ratio.
Let's solve it step by step:
- Start with the given proportion: 21/28 = x/24.
- Simplify the left side of the proportion by dividing both numbers by 7, which gives 3/4 = x/24.
- Cross multiply: 3 * 24 = 4 * x, resulting in 72 = 4x.
- Divide both sides by 4 to isolate x and solve for it: x = 72 / 4, which simplifies to x = 18.