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?
plz help asap
Answers
Answer :-
Let helena makes x loaves of breads and y batches of muffins .
so,
→ 3.5x + 2.5y = 17
→ (35/10)x + (25/10)y = 17
→ 35x + 25y = 170
→ 5(7x + 5y) = 170
→ 7x + 5y = 34 -------------- Eqn.(1)
and,
→ 0.75x + 0.75y = 4.5
→ 0.75(x + y) = 4.5
→ x + y = 6 ------------ Eqn.(2)
Multiply Eqn.(2) by 5 and subtracting the result from Eqn.(1)
→ (7x + 5y) - 5(x + y) = 34 - 5*6
→ 7x - 5x + 5y - 5y = 34 - 30
→ 2x = 4
→ x = 2 .
putting value of x in Eqn.(2),
→ 2 + y = 6
→ y = 6 - 2
→ y = 4 .
therefore, helena can bake 2 loaves of bread and 4 batches of muffins with 17 cups of flour and 4.5 cups of sugar.
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Answer:
2 loaves of bread and 4 batches of muffins