At her juice parlor, Mrs. Jones makes a different amount of fruit punch each day by mixing grape juice and peach juice. The table
shows the amount of grape juice, g, and the amount of peach juice, p, Mrs. Jones uses to make different quantities of the punch.
Amount of
Grape Juice, g
(in liters)
11.5
17.5
20.5
26.5
34.5
Amount of
Peach Juice, p
(in liters)
6.9
10.5
12.3
15.9
20.7
Which equation represents the proportional relationship between the amounts of grape juice and peach juice?
To determine the equation that represents the proportional relationship between the amounts of grape juice and peach juice, we need to calculate the ratio of grape juice to peach juice for each combination.
Ratio = Amount of Grape Juice / Amount of Peach Juice
For the given data, the ratios are as follows:
- Ratio for the first combination: 11.5/6.9 = 1.67
- Ratio for the second combination: 17.5/10.5 = 1.67
- Ratio for the third combination: 20.5/12.3 = 1.67
- Ratio for the fourth combination: 26.5/15.9 = 1.67
- Ratio for the fifth combination: 34.5/20.7 = 1.67
As the ratios are all the same (approximately 1.67), we can conclude that the relationship between the amounts of grape juice and peach juice is proportional.
The equation that represents the proportional relationship can be written as:
Grape Juice = a * Peach Juice
where 'a' is the constant ratio, which in this case is approximately 1.67.
So, the equation representing the proportional relationship between the amounts of grape juice (g) and peach juice (p) is:
g = 1.67p