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? a. 2 loaves of bread and 4 batches of muffins b. 3 loaves of bread and 3 batches of muffins c. 4 loaves of bread and 2 batches of muffins d. 5 loaves of bread and 1 batch of muffins
Mathematics · High School · Tue Nov 03 2020
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let batches of loaf of bread is x and batches of muffins is y
so, according to the question, 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins and 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins
now, Helena has 17 cups of flour and 4.5 cups of sugar
so, 3.5x+2.5y=17 …………….equation(1)
0.75x+0.75y=4.5 ………………equation(2)
from equation (2), 0.75 take as common:-
0.75(x+y)=4.5
x+y=4.5/0.75
x+y=6 ………………..equation (3)
from equation (3)
y=6-x ……………equation(4)
put this value of y in equation (1)
3.5x+2.5(6-x)=17
3.5x+15-2.5x=17
x=17-15
x=2
put this value of x in equation (4)
y=6-2
y=4
so, 2 loaves of bread and 4 batches of muffins.