a restaurant makes a special citrus dressing for its salads here is ingredients are mixed 1/3 of the mixture is oil 1/6 of the mixture is vinegar 1/4 of the mixture is orange juice 1/4 of the mixture is lemon juice when the ingredients are mixed in the same ratio as shown above every batch of dressing taste the same study the measurements for the batch in the table fill in the blank so that every batch will taste the same batch number one or is one cup vinegar is x cup orange juice 3/4 cup lemon juice x cup
The ratios of the ingredients is
4:2:3:3 = 1 : 1/2 : 3/4 : 3/4
Well, well, well, it seems like we've got a dressing conundrum here. Let's break it down!
According to the given ratios, we know that 1/3 of the mixture is oil, 1/6 is vinegar, 1/4 is orange juice, and 1/4 is lemon juice. Now, we need to figure out the missing measurements!
Let's start with batch number one. We already know that it consists of one cup vinegar, 3/4 cup lemon juice, and X cups of orange juice. To make it taste the same as every other batch, we need to maintain the ratios.
Given that 1/6 of the mixture is vinegar, we can set up the equation:
1/6 = 1 cup vinegar / Total mixture
Now, to find the value of the total mixture, we can cross multiply:
Total mixture = 1 cup vinegar * 6 / 1
Total mixture = 6 cups
Since the total mixture is 6 cups, and 1/4 of it is orange juice, we can calculate:
1/4 = X cups orange juice / 6 cups total mixture
Cross multiplying gives us:
X cups orange juice = (1/4) * 6 cups
X cups orange juice = 1.5 cups
So, to make the batch number one taste the same, it should contain 1 cup vinegar, 1.5 cups orange juice, and 3/4 cup lemon juice.
Now go forth and create some citrusy dressing magic! Enjoy!
To find the missing measurements for batch number one, we need to ensure that the ratio of the ingredients remains the same as the given ratio.
Given information:
- 1/3 of the mixture is oil
- 1/6 of the mixture is vinegar
- 1/4 of the mixture is orange juice
- 1/4 of the mixture is lemon juice
Let's break it down step-by-step:
Step 1: Determine the total amount of the mixture.
To find the common denominator for the ratio fractions, we can use 12 as the denominator.
- 1/3 of the mixture is oil: (1/3) * 12 = 4 cups of oil
- 1/6 of the mixture is vinegar: (1/6) * 12 = 2 cups of vinegar
- 1/4 of the mixture is orange juice: (1/4) * 12 = 3 cups of orange juice
- 1/4 of the mixture is lemon juice: (1/4) * 12 = 3 cups of lemon juice
Step 2: Calculate the amount of missing ingredients.
- Since the total amount of the mixture is 12 cups, we can subtract the amounts of oil, vinegar, orange juice, and lemon juice to find out how much space is left for the missing ingredients.
12 cups - (4 cups of oil + 2 cups of vinegar + 3 cups of orange juice + 3 cups of lemon juice) = 12 - (4+2+3+3) = 12 - 12 = 0
Therefore, the missing measurements for batch number one are:
- 0 cups of vinegar
- 0 cups of orange juice
- 0 cups of lemon juice
This means that batch number one does not contain any vinegar, orange juice, or lemon juice. It consists only of 4 cups of oil.
To figure out the missing values, we need to consider the given ratios of the ingredients in the salad dressing.
Let's start by identifying the total number of parts in the mixture. From the ratios given, we can see that the dressings consist of 1/3 oil + 1/6 vinegar + 1/4 orange juice + 1/4 lemon juice.
To combine these fractions, we need to find a common denominator. In this case, the least common denominator is 12. Therefore, we can convert the fractions as follows:
1/3 = 4/12
1/6 = 2/12
1/4 = 3/12
1/4 = 3/12
So, the total number of parts is 4/12 + 2/12 + 3/12 + 3/12 = 12/12, which is equal to 1.
Now, let's assign the values for the missing quantities based on the given ratios:
For batch number one:
1 cup vinegar = x cup orange juice
3/4 cup lemon juice = x cup
Since the total number of parts is 1, we can find the values for x by equating the fractions:
1 cup vinegar / (x cup orange juice) = (3/4 cup lemon juice) / x cup
To solve the equation, we can cross-multiply:
1 * x cup = (3/4 cup) * (x cup orange juice)
3/4 * x cup
Now, let's solve for x:
x = (3/4) / 1
x = 3/4
Therefore, for batch number one, we find that x is equal to 3/4 cup of orange juice.
To summarize:
For batch number one:
1 cup vinegar = 3/4 cup orange juice
3/4 cup lemon juice = 3/4 cup
Every batch will taste the same when the measurements are as follows:
Batch number one:
1 cup vinegar = 3/4 cup orange juice
3/4 cup lemon juice = 3/4 cup