Select all of the following that are a direct variation.
Songs are 99 cents each to download.
Tickets for rides at the fair are $1 each.
Arcade games are 50 cents or $1.
To go tubing it is $5 to rent the tube and $7 for each hour
A direct variation is a mathematical relationship between two variables in which one variable is a constant multiple of the other. Let's analyze each option:
1. Songs are 99 cents each to download.
- This is a direct variation since the cost of downloading songs is directly proportional to the number of songs purchased.
2. Tickets for rides at the fair are $1 each.
- This is also a direct variation since the cost of tickets is directly proportional to the number of tickets purchased.
3. Arcade games are 50 cents or $1.
- This option is not a direct variation as there are two different prices for arcade games, which means the price is not directly proportional to the number of games played.
4. To go tubing it is $5 to rent the tube and $7 for each hour.
- This option is not a direct variation either since the cost of tubing involves both a fixed component (renting the tube) and a variable component (number of hours).
Therefore, the direct variations among the given options are songs being 99 cents each to download and tickets for rides at the fair being $1 each.
A direct variation is a mathematical relationship between two variables where one variable is a constant multiple of the other variable. In other words, if we can write the relationship between the two variables in the form y = kx, where k is a constant, then it is a direct variation.
Let's go through each option:
1. Songs are 99 cents each to download.
In this case, the cost of songs depends on the number of songs downloaded. Since the cost is directly proportional to the number of songs (each song costs 99 cents), this is a direct variation.
2. Tickets for rides at the fair are $1 each.
Similar to the songs, the cost of tickets is directly proportional to the number of tickets purchased. Each ticket costs $1, so this is also a direct variation.
3. Arcade games are 50 cents or $1.
This option has two different prices, 50 cents and $1, which means the cost of arcade games is not consistent. Therefore, this is not a direct variation.
4. To go tubing it is $5 to rent the tube and $7 for each hour.
Here, we have two variables: the rental fee and the number of hours. The rental fee of $5 is constant, but the hourly charge of $7 changes with the number of hours. Thus, this is not a direct variation.
So, the direct variations in the given options are:
- Songs are 99 cents each to download.
- Tickets for rides at the fair are $1 each.