Sure, let's solve these problems step-by-step:
### Problem 1
The ratio of tomatoes to red apples is 2:5. If there are 20 tomatoes, how many red apples are there?
1. Understand the ratio: The ratio [tex]\( 2:5 \)[/tex] means that for every 2 tomatoes, there are 5 red apples.
2. Set up the proportion: You can write the ratio as a fraction:
[tex]\[
\frac{\text{tomatoes}}{\text{red apples}} = \frac{2}{5}
\][/tex]
3. Plug in the given number of tomatoes: We know there are 20 tomatoes, so let’s set up the proportion with the known quantity:
[tex]\[
\frac{20}{\text{red apples}} = \frac{2}{5}
\][/tex]
4. Solve for the number of red apples:
Cross-multiply to find the number of red apples:
[tex]\[
20 \times 5 = 2 \times \text{number of red apples}
\][/tex]
Simplify:
[tex]\[
100 = 2 \times \text{number of red apples}
\][/tex]
Divide both sides by 2:
[tex]\[
50 = \text{number of red apples}
\][/tex]
Thus, there are 50 red apples.
### Problem 2
The ratio of berries to oranges is 10:1. If there are 25 oranges, how many berries are there?
1. Understand the ratio: The ratio [tex]\( 10:1 \)[/tex] means that for every 1 orange, there are 10 berries.
2. Set up the proportion: You can write the ratio as a fraction:
[tex]\[
\frac{\text{berries}}{\text{oranges}} = \frac{10}{1}
\][/tex]
3. Plug in the given number of oranges: We know there are 25 oranges, so let’s set up the proportion with the known quantity:
[tex]\[
\frac{\text{berries}}{25} = \frac{10}{1}
\][/tex]
4. Solve for the number of berries:
Since the ratio is 10 berries per orange, simply multiply the number of oranges by 10:
[tex]\[
\text{number of berries} = 10 \times 25
\][/tex]
Simplify:
[tex]\[
\text{number of berries} = 250
\][/tex]
Thus, there are 250 berries.
In conclusion:
1. There are 50 red apples.
2. There are 250 berries.
