Answer:
The equation c = [tex]\frac{3}{7}[/tex] f represents the relationship between c and f ⇒ 3rd answer
Step-by-step explanation:
Let us use the ratio method to find the equation that represents the relation between c and f
∵ Clare uses [tex]9\frac{1}{3}[/tex] cups of flour to make 4 cakes
∵ Noah will follow the same recipe
∵ Noah will use f cups of flour to make c cakes
By using the ratio method
→ Name : Cup : Cake
→ Clare : [tex]9\frac{1}{3}[/tex] : 4
→ Noah : f : c
By using cross multiplication
∴ [tex]9\frac{1}{3}[/tex] × c = 4 × f
∴ [tex]9\frac{1}{3}[/tex] c = 4 f
- Divide both sides by [tex]9\frac{1}{3}[/tex]
∴ c = 4 f ÷ [tex]9\frac{1}{3}[/tex]
- Change [tex]9\frac{1}{3}[/tex] to improper fraction by multiplying 9 by 3 and
then add 1 to the product (9 × 3 = 27 + 1 = 28)
∵ [tex]9\frac{1}{3}[/tex] = [tex]\frac{28}{3}[/tex]
∴ c = 4 f ÷ [tex]\frac{28}{3}[/tex]
- Change ÷ to × and reciprocal [tex]\frac{28}{3}[/tex]
∴ c = 4 f × [tex]\frac{3}{28}[/tex]
∴ c = [tex]\frac{12}{28}[/tex] f
- Simplify it by dividing up and down by 4
∴ c = [tex]\frac{3}{7}[/tex] f
The equation c = [tex]\frac{3}{7}[/tex] f represents the relationship between c and f
