Question

Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint. Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint. How does Tina's favorite shade of teal compare to Tyler's favorite shade of teal?

Answer 1

Tina's favorite shade is more blue than Tyler's

Answer 2

We have been given that Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint and Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.

We can express the ratio of blue paint to green paint for both Tina as well as Tyler's favorite shades of teal as shown below.

For Tina:
`(7)/(5)`

For Tyler:
`(5)/(7)`

In order to compare the two ratios, we will have to make the denominators equal. Let us make denominators equal for both these ratios.

For Tina:
`(7\cdot7)/(5\cdot7)=(49)/(35)`

For Tyler:
`(5\cdot5)/(7\cdot5)=(25)/(35)`

Therefore, we can see that for equal amount of Green paint, Tina's favorite shade of teal contains
`(49)/(25)` times, that is almost twice the Blue paint that Tyler's favorite shade of teal contains.