Question

Each set of (x, y) values represent a set of equivalent ratios. Find the ratio of x to y for each set to determine which set describes the proportional relationship: 40.5 ounces of nuts to 48.6 ounces of raisins.
A) (5, 7)(60, 84)(47, 65.8)
B) (36, 48.6)(2, 2.7)(12, 16.2)
C) (3, 3.9)(65, 84.5)(24, 31.2)
D) (11, 13.2)(99, 118.8)(20, 24)

Answer 1

Solution:

$\frac{x}{y}=\frac{40.5}{48.6}$=$\frac{45}{54}=\frac{5}{6}$

If you will choose among the options

Option A contains (5,7) as the ratio is (5,6) , so incorrect option.

Option B contain (2,2.7) not equivalent to (5,6), so Incorrect option.

Option C contain (3,3.9) which is not equivalent to (5,6), so incorrect option.

Now coming to option (D) , we see that

$\frac{11}{13.2}=\frac{5}{6},\frac{99}{118.8}=\frac{90}{108}=\frac{5}{6},\frac{20}{24}=\frac{5}{6}$

All of them are equivalent to (5,6) i.e 40.5 ounces of nuts to 48.6 ounces of raisins.

So , Option (D) (11, 13.2)(99, 118.8)(20, 24) is correct option.

Answer 2

Answer: The correct set is choice D.

We are looking for the same ratio with the given set of measurements. So lets start by determine the ratio of nuts to raisins. It is 40.5 to 48.6 or reduced it is 5 to 6. If you divide the fraction, you get the decimal 0.83333.

Only one of the relationships given has the same ratio. It is choice D.  11 to 13.32 can be divided to get 0.83333.