Jessica is baking a cake. The recipe says that she has to mix 96 grams of sugar to the flour. Jessica knows that 1 cup of this particular sugar has a mass of 128 grams. She added one over two of a cup of sugar to the flour. Should Jessica add more sugar to make the exact recipe, or did she go over and by what amount?
Last semester, a certain professor gave 41 As out of 215 grades. If one of the professor's students from last semester were selected randomly, what is the probability that student received an A? (Assume that each student receives one grade.)
To determine if Jessica needs to add more sugar or if she has added too much, we need to compare the amount of sugar she added with the amount stated in the recipe.
The recipe calls for 96 grams of sugar to be added to the flour. We know that 1 cup of this particular sugar weighs 128 grams.
Jessica added one over two of a cup of sugar, which is equivalent to 0.5 cups.
To find out how much sugar Jessica added, we can multiply the weight of 1 cup of sugar by the fraction she used (0.5 cups).
Weight of sugar added = 128 grams/cup * 0.5 cups = 64 grams
Now we can compare the actual amount of sugar Jessica added (64 grams) with the amount specified in the recipe (96 grams) to determine if she needs to add more or if she added too much.
If Jessica added less than 96 grams, she needs to add more sugar to make the exact recipe. The difference between the amount she added and the required amount would be:
Difference = 96 grams - 64 grams = 32 grams
Therefore, Jessica needs to add an additional 32 grams of sugar to make the exact recipe.
To determine whether Jessica needs to add more sugar or if she has gone over the amount required in the recipe, we need to compare the amount of sugar she added to the amount specified in the recipe.
Let's break down the information given:
1 cup of sugar = 128 grams
The recipe calls for 96 grams of sugar to be mixed with the flour.
Jessica added one-half (1/2) a cup of sugar. We need to calculate the mass of the sugar she added.
To find out the mass of sugar Jessica added, we can use the ratio of sugar to cups:
1 cup of sugar = 128 grams
Using this ratio, we need to determine the amount of sugar in 1/2 cup. We can set up a proportion as follows:
1 cup of sugar = 128 grams
1/2 cup of sugar = x grams (where x is the unknown amount of grams in 1/2 cup)
Now, cross-multiply and solve for x:
(1/2) * 128 = x
x = 64 grams
Therefore, Jessica added 64 grams of sugar to the flour.
Next, we compare the amount Jessica added (64 grams) to the amount specified in the recipe (96 grams).
If Jessica's amount is less than 96 grams, she needs to add more sugar. If it is equal to or greater than 96 grams, she has either reached the exact recipe or gone over the required amount.
In this case, 64 grams is less than 96 grams. Hence, Jessica needs to add more sugar to make the exact recipe.
To calculate the amount she needs to add, we subtract the amount she already added (64 grams) from the required amount (96 grams):
96 grams - 64 grams = 32 grams
Therefore, Jessica needs to add an additional 32 grams of sugar to make the exact recipe.