1. suppose you pay $24 for a pair of shoes that originally cost $40. what was the percent of decrease in price for the shoes? set up an equation, arrive at your answer, and check your work. then clearly state your answer 2. set up the following word problem as a proportion and solve. then write your answer as a complete sentence. a health department estimates that 6 vials of malaria serum will treat 100 people. at this rate, how many vials are required to treat 150 people?

1) The shoes were purchased at a 40% discount.

2) In order to treat 150 patients, the health department will require 9 vials of the malaria serum.

Step-by-step explanation:

1) If the original cost of the pair of shoes was $40, and you paid $24, then we want to set up a proportion to solve for the discounted percentage.

The discounted percentage is what you DID NOT pay, therefore we will find the amount of money saved first before setting up our proportion

$40 - $24 = $16

Meaning you did not pay that extra $16

Using that deficit, let's set up a proportion in terms of the total:

16/40 = 0.4

To find the percentage that was discounted we must multiply our proportion by 100%

0.4 *100% = 40%

Therefore, the shoes you had bought were on sale for 40% off.

2) If the health department expects 6 vials of malaria serum to treat 100 patients then our proportion of vials to patients becomes

6/100

To solve for how many vials will be required to treat 150 patients, we must equate our expected proportion to one with those 150 patients

6/100 = x/150          Where x denotes the number of vials needed.

                                Multiply both sides by 150 to isolate x

900/100 = x             Reduce the fraction

9 = x

Therefore, in order to treat 150 patients, the health department will require 9 vials of the malaria serum.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.