Question

Mr. Crane and Ms. Finch are next-door neighbors. They both have beautiful gardens with feeders that attract wildlife. Mr. Crane uses 2 cups of sunflower seeds for every 6 cups of birdseed in his feeders. Ms. Finch uses 3 cups of sunflower seeds for every 5 cups of birdseed in her feeders. Whose feeder has a greater ratio of sunflower seeds to birdseed?

Answer 1

Ms finch has the higher ratio

Explanation:

Given ratios 2 : 6 and 3 : 5, you want to know which is greater.

Comparison

There are several ways to compare ratios. You can express them over a common denominator, compare them to a common value, convert them to decimal, subtract one from the other.

Common denominator

2 : 6 vs 3 : 5 = 10 : 30 vs 18 : 30

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

Common value

2 : 6 vs 3 : 5

We can compare each of these to 1/2.

2 : 6 < 3 : 6 = 1/2

3 : 5 > 2.5 : 5 = 1/2

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

Decimal conversion

2 : 6 ≈ 0.333

3 : 5 = 0.600

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

Subtraction

2/6 -3/5 = (10 -18)/(30) = -8/30 so the second ratio is higher

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.