Tony is baking cakes and loaves of bread for a family reunion. His cake recipe uses 5 cups of flour for each cake, and his bread recipe uses 6 cups of flour for each loaf. He has 90 cups of flour on hand.
Let c represent the number of cakes and b represent the number of loaves of bread that Tony bakes.
Create the inequality that symbolizes this situation, and then answer the question below.
c +
b ≤
Can Tony bake 8 cakes and 9 loaves of bread without buying more flour?
The inequality that represents this situation is: 5c + 6b ≤ 90
To determine if Tony can bake 8 cakes and 9 loaves of bread without buying more flour, we substitute c = 8 and b = 9 into the inequality:
5(8) + 6(9) ≤ 90
40 + 54 ≤ 90
94 ≤ 90
Since 94 is greater than 90, Tony cannot bake 8 cakes and 9 loaves of bread without buying more flour.
To create the inequality, we can use the given information about the amount of flour used in each cake and loaf of bread.
The cake recipe uses 5 cups of flour for each cake, and the bread recipe uses 6 cups of flour for each loaf. Let's represent the number of cakes as 'c' and the number of loaves of bread as 'b'.
The total amount of flour used for cakes can be represented as 5c (5 cups of flour per cake multiplied by the number of cakes 'c').
The total amount of flour used for bread can be represented as 6b (6 cups of flour per loaf multiplied by the number of loaves of bread 'b').
The total amount of flour used in all the cakes and loaves of bread should not exceed the available flour, which is 90 cups.
Therefore, the inequality is:
5c + 6b ≤ 90
Now, let's check if Tony can bake 8 cakes and 9 loaves of bread without buying more flour.
Plug in the values into the inequality:
5(8) + 6(9) ≤ 90
40 + 54 ≤ 90
94 ≤ 90
The statement "94 ≤ 90" is false, so Tony cannot bake 8 cakes and 9 loaves of bread without buying more flour.