Answer:
a. The equation is s = [tex]\frac{1}{3}[/tex] w
b. [tex]1\frac{5}{12}[/tex] cups of sugar will be needed to follow the recipe
Step-by-step explanation:
The equation of the direct proportional relation is y = k x, where
- k is the constant of proportionality
We can find the value of k by using the initial values of x and y
Let us use this rule to solve the question
∵ In the recipe for 1/2 cup of sugar for every 1 1/2 cups of water
→ That means the number of cups of sugar is in proportion to the
number of cups of water
∵ s represents the number of cups of sugar
∵ w represents the number of cups of water
∴ s ∝ w ⇒ (∝ a sign of proportion)
∴ s = k w ⇒ k is the constant of proportionality
∵ s = [tex]\frac{1}{2}[/tex] and w = [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
Substitute the values of s and w in the equation above to find k
∵ [tex]\frac{1}{2}[/tex] = k × [tex]\frac{3}{2}[/tex]
→ Multiply both sides by 2 to cancel the denominators
∴ 1 = 3 k
→ Divide both sides by 3 to find k
∴ [tex]\frac{1}{3}[/tex] = k
∴ The equation is s = [tex]\frac{1}{3}[/tex] w ⇒ a.
→ We need to find the number of sugar cups for 4 1/4 cups of water
∵ w = [tex]4\frac{1}{4}=\frac{17}{4}[/tex]
∵ s = [tex]\frac{1}{3}[/tex] w
→ Substitute w by 5/4
∴ s = [tex]\frac{1}{3}[/tex] × [tex]\frac{17}{4}[/tex]
∴ s = [tex]\frac{17}{12}=1\frac{5}{12}[/tex]
∴ [tex]1\frac{5}{12}[/tex] cups of sugar will be needed to follow the recipe ⇒ b.
