Lionel has at most 68/8 cups of flour to bake cookies and a cake. Lionel uses 7/4 cups of flour to make the cake. If each batch of cookies takes 3/2 cups of flour, how many batches of cookies, x, can Lionel bake? Select the inequality that includes the maximum number of batches of cookies Lionel can bake.
A. x ≥ 49/12
B. x ≤ 49/12
C. x ≥ 49/8
D. x ≤ 49/8
To find the maximum number of batches of cookies Lionel can bake, we need to find the number of batches that will use up the remaining flour after making the cake.
First, we need to subtract the amount of flour used for the cake from the total amount of flour Lionel has: 68/8 cups - 7/4 cups = 34/8 cups - 14/8 cups = 20/8 cups.
Next, we need to divide the remaining amount of flour by the amount of flour used for each batch of cookies to find the maximum number of batches Lionel can bake: 20/8 cups / 3/2 cups/batch = (20/8 cups) * (2/3 cups/batch) = 40/24 batches = 5/3 batches.
Since Lionel can only bake a whole number of batches, the maximum number of batches of cookies Lionel can bake is 1 batch. Therefore, the correct inequality is x ≤ 1.
So the answer is D. x ≤ 49/8.
wrong
Apologies for the mistake. Let's correct it:
To find the maximum number of batches of cookies Lionel can bake, we need to divide the remaining amount of flour (after making the cake) by the amount of flour used for each batch of cookies.
First, we need to subtract the amount of flour used for the cake from the total amount of flour Lionel has: 68/8 cups - 7/4 cups = 34/8 cups - 14/8 cups = 20/8 cups.
Next, we need to divide the remaining amount of flour by the amount of flour used for each batch of cookies to find the maximum number of batches Lionel can bake: (20/8 cups) / (3/2 cups/batch) = (20/8 cups) * (2/3 cups/batch) = 40/24 batches = 5/3 batches.
Since Lionel can only bake a whole number of batches, the maximum number of batches of cookies Lionel can bake is 1 batch.
So the correct inequality is x ≤ 1.
Therefore, the answer is D. x ≤ 49/8.