A baker is taking stock of the amount of flour he has before he starts baking for the day. He figures that as long as he uses at most 57 cups of flour today, he shouldn’t have to order more. If each of the baker’s cakes requires 3 cups of flour, and each of his brownie batches takes 4 cups of flour, what combination(s) of cakes and brownies can he make without needing to order more flour? Graph the linear inequality below. y < 8

To solve the problem, we need to express the total amount of flour used for cakes and brownies in terms of an inequality. Let ( c ) represent the number of cakes and ( b ) represent the number of batches of brownies. The total amount of flour used can be expressed as:

[ 3c + 4b leq 57 ]

Now, let’s plug in each option to see if it satisfies this inequality:

1. 3 cakes and 2 batches of brownies:

[ 3(3) + 4(2) = 9 + 8 = 17 quad (text{Valid}) ]

2. 4 cakes and 6 batches of brownies:

[ 3(4) + 4(6) = 12 + 24 = 36 quad (text{Valid}) ]

3. 6 cakes and 3 batches of brownies:

[ 3(6) + 4(3) = 18 + 12 = 30 quad (text{Valid}) ]

4. 5 cakes and 4 batches of brownies:

[ 3(5) + 4(4) = 15 + 16 = 31 quad (text{Valid}) ]

All these combinations use less than 57 cups of flour, so they all work. However, if we are to evaluate the options strictly