Answer :
- Set up the proportion: $\frac{7}{5} = \frac{21}{x}$.
- Cross-multiply: $7x = 5 \times 21$.
- Solve for $x$: $x = \frac{5 \times 21}{7}$.
- Simplify to find the value of $x$: $x = 15$. The final answer is $\boxed{15}$.
### Explanation
1. Understanding the Problem
We are given the ratio $7:5$ and we want to find an equivalent ratio of the form $21:x$. This means we need to find the value of $x$ such that the two ratios are proportional. In other words, we want to find $x$ such that $\frac{7}{5} = \frac{21}{x}$.
2. Cross-Multiplication
To solve for $x$, we can cross-multiply. This gives us $7x = 5 \times 21$.
3. Isolating x
Now, we can solve for $x$ by dividing both sides of the equation by 7: $$x = \frac{5 \times 21}{7}$$.
4. Simplifying the Expression
We can simplify this expression by first dividing 21 by 7, which gives us 3. Then, we multiply 5 by 3 to get 15. Therefore, $x = 15$. So, the equivalent ratio is $21:15$.
5. Final Answer
Therefore, $7:5$ is equivalent to $21:15$. The missing number is $\boxed{15}$.
### Examples
Ratios and proportions are used in everyday life, such as when scaling recipes. If a recipe calls for 7 cups of flour and 5 cups of sugar, and you want to make a larger batch using 21 cups of flour, you can use proportions to find out how much sugar you need. In this case, you would need 15 cups of sugar to maintain the same ratio and taste.
- Cross-multiply: $7x = 5 \times 21$.
- Solve for $x$: $x = \frac{5 \times 21}{7}$.
- Simplify to find the value of $x$: $x = 15$. The final answer is $\boxed{15}$.
### Explanation
1. Understanding the Problem
We are given the ratio $7:5$ and we want to find an equivalent ratio of the form $21:x$. This means we need to find the value of $x$ such that the two ratios are proportional. In other words, we want to find $x$ such that $\frac{7}{5} = \frac{21}{x}$.
2. Cross-Multiplication
To solve for $x$, we can cross-multiply. This gives us $7x = 5 \times 21$.
3. Isolating x
Now, we can solve for $x$ by dividing both sides of the equation by 7: $$x = \frac{5 \times 21}{7}$$.
4. Simplifying the Expression
We can simplify this expression by first dividing 21 by 7, which gives us 3. Then, we multiply 5 by 3 to get 15. Therefore, $x = 15$. So, the equivalent ratio is $21:15$.
5. Final Answer
Therefore, $7:5$ is equivalent to $21:15$. The missing number is $\boxed{15}$.
### Examples
Ratios and proportions are used in everyday life, such as when scaling recipes. If a recipe calls for 7 cups of flour and 5 cups of sugar, and you want to make a larger batch using 21 cups of flour, you can use proportions to find out how much sugar you need. In this case, you would need 15 cups of sugar to maintain the same ratio and taste.
