Question

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?

Answer 1

Helena can make 2 loaves of  bread and 4 batches of muffins.

Answer 2

Helena can bake 2 loaves of bread and 4 batches of muffins.

Explanation:

Suppose, Helena can bake
`x` loaves of bread and
`y` batches of muffins.

She needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins and she has total 17 cups of flour.

So, the first equation will be:
`3.5x+2.5y=17 .....................(1)`

She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins and she has total 4.5 cups of sugar.

So, the second equation will be:
`0.75x+0.75y=4.5......................(2)`

From equation(2), we will get.......

`0.75y=4.5-0.75x\\ \\ y=(4.5)/(0.75)-(0.75x)/(0.75)\\ \\ y=6-x`

Substituting this
`y=6-x` into equation (1)...........

`3.5x+2.5(6-x)=17\\ \\ 3.5x+15-2.5x=17\\ \\ x+15=17\\ \\ x=17-15=2`

When
`x=2`, then
`y=6-2=4`

So, Helena can bake 2 loaves of bread and 4 batches of muffins.