Question

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Answer 1

Part a)

The equation of the situation is:

• y = 8x

Part b)

If the recipe calls for 16 ounces of flour, the number of ounces of sugar will be:

• x = 2

Explanation:

Part a) Determining the equation

Given the number of ounces of flour 'y' is proportional to the number of ounces of sugar 'x'.

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

• Here, k is the constant of direct variation.

Given

y = 48

x = 6

y = kx

k = y/x

k = 48/6

k = 8

Thus, the constant of direct variation = k = 8

Therefore, the equation that represents the equation

y = kx

substituting k = 8 in the equation

y = 8x

Therefore, the equation of the situation is:

• y = 8x

Part b) Determining the ounces of sugar i.e. 'x' when ounces of

flour = y = 16

Given

y = 16

k = 8

Ounces of sugar = x = ?

Using the equation

y = 8x

substituting y = 16

16 = 8x

8x = 16

dividing both sides by 8

x = 2

Therefore, if the recipe calls for 16 ounces of flour, the number of ounces of sugar will be:

• x = 2