Ratios, rates, proportional relationships, and units

How many yards are equivalent to `"1,116"` inches?
(`1` yard = `36` inches)

Answer: `31`

To convert inches to yards, you divide the number of inches by the number of inches in a yard. So, you calculate `frac("1,116 inches") (("36 inches")/("yard"))`, which equals `31` yards.

Out of `300` seeds that were planted, `80%` sprouted. How many of these seeds sprouted?

Answer: 240

It is given that `80%` of the `300` seeds sprouted. Therefore, the number of seeds that sprouted can be calculated by multiplying the number of seeds that were planted by `80/100`, which gives `300 xx (80/100)`, or `240`.

The ratio of the length of line segment `XY` to the length of line segment `ZV` is `6` to `1`. If the length of line segment `XY` is `102` inches, what is the length, in inches, of line segment `ZV`?

A) `17`

B) `96`

C) `102`

D) `612`

Answer: A

Set up a proportion based on the given ratio: `(XY)/(ZV) = 6/1`.

Substitute the known length of `XY`: `102/ZV = 6/1`.

To solve for `ZV`, you can cross-multiply to get `102 = 6 xx ZV`, and then divide by `6`, which gives `ZV=17` inches.

Brian saves `2/5` of the `$215` he earns each week from his job. If Brian continues to save at this rate, how much money, in dollars, will Brian save in `9` weeks?

Answer: `774`

First, calculate Brian's weekly savings: `(2/5) xx 215 = $86`.

Then, multiply the weekly savings by the number of weeks: `86 xx 9 = 774`. Brian will save `$774` in `9` weeks.