helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs…

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. helena has 17 cups of flour and 4.5 cups of sugar available for baking. which combination of loaves of bread and batches of muffins could helena bake? 2 loaves of bread and 4 batches of muffins 3 loaves of bread and 3 batches of muffins 4 loaves of bread and 2 batches of muffins 5 loaves of bread and 1 batch of muffins

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. helena has 17 cups of flour and 4.5 cups of sugar available for baking. which combination of loaves of bread and batches of muffins could helena bake? 2 loaves of bread and 4 batches of muffins 3 loaves of bread and 3 batches of muffins 4 loaves of bread and 2 batches of muffins 5 loaves of bread and 1 batch of muffins

Answer

Explanation:

Step1: Calculate flour - usage for each option

Let $x$ be the number of loaves of bread and $y$ be the number of batches of muffins. The flour - usage formula is $F = 3.5x+2.5y$. For option 1 ($x = 2,y = 4$): $F_1=3.5\times2 + 2.5\times4=7 + 10=17$ cups. For option 2 ($x = 3,y = 3$): $F_2=3.5\times3+2.5\times3=(3.5 + 2.5)\times3=6\times3 = 18$ cups. For option 3 ($x = 4,y = 2$): $F_3=3.5\times4+2.5\times2=14 + 5=19$ cups. For option 4 ($x = 5,y = 1$): $F_4=3.5\times5+2.5\times1=17.5+2.5 = 20$ cups.

Step2: Calculate sugar - usage for each option

The sugar - usage formula is $S=0.75x + 0.75y$. For option 1 ($x = 2,y = 4$): $S_1=0.75\times2+0.75\times4=0.75\times(2 + 4)=4.5$ cups. For option 2 ($x = 3,y = 3$): $S_2=0.75\times3+0.75\times3=0.75\times(3 + 3)=4.5$ cups. Since we need to satisfy both flour and sugar constraints and option 2 exceeds the flour limit, while option 1 satisfies both the 17 - cup flour limit and 4.5 - cup sugar limit.

Answer:

2 loaves of bread and 4 batches of muffins