Numbers & Operations
Tackling The Real World Items
One last step method to learn:
Step 1: Determine what the item is really asking you to solve.
Step 2: Create an equation.
Step 3: Solve the equation.
The Real World Items in Slow Motion
All together now:
7. Experts say that of 300 mushrooms, 25% are poisonous, and of all poisonous mushrooms, 80% are fatal. How many mushrooms are fatally poisonous?
(A) 80
(B) 75
(C) 60
(D) 100
(E) 275
Step 1: Determine what the item is really asking you to solve.
The item wants you to compare parts of a whole, so you need to set up a proportion. This item is about double percents, so you need to apply your knowledge of this concept. Be careful when taking the percent of the second value.
Step 2: Create an equation.
First you need to find out how many mushrooms are poisonous, which means taking 25% of 300. Then you need to determine what 80% of the poisonous mushrooms is, not the total number of mushrooms. So really, you are dealing with two equations here:
25% of 300 = poisonous mushrooms
80% of poisonous mushrooms = fatally poisonous mushrooms
You can also write out the order of operations if it helps you. If you sketch out a plan, the task becomes much easier.
Step 3: Solve the equation.
Set up a proportion to find 25% of 300:
(25%)(300) =
(0.25)(300) = 75
You have 75 poisonous mushrooms.
Now take 80% of 75:
(80%)(75) =
(0.80)(75) = 60
So of 75 poisonous mushrooms, 60 are fatal. Answer choice C is correct.
Guided Practice
Try this one on your own:
5. There are 48 cars in a parking lot. One-third of them are blue, 24 are red, and the rest are white. What is the ratio of white cars to blue cars?
(A) 1:2
(B) 1:3
(C) 1:6
(D) 2:3
(E) 5:6
Step 1: Determine what the item is really asking you to solve.
What do you have to find first to solve this item? What do you need to find the ratio? Do you have all the numbers?
Step 2: Create an equation.
Do you know the total number of each color? How can you find the missing numbers? Do you have to find the ratios of all the cars or just of white to blue?
Step 3: Solve the equation.
Be careful with your numbers. How do you find one-third of the whole? What is the whole in this item?
Guided Practice: Explanation
Step 1: Determine what the item is really asking you to solve.
The item ultimately asks you to find the ratio of white cars to blue cars. That means that you should figure out the actual numbers of cars, then compare them to each other.
Step 2: Create an equation.
In this case, you need to find out how many white, red, and blue cars there are in the parking lot. First you need to find the number of blue cars:
Then find the number of white cars:
white = 48 – (blue + red)
Then you can determine the ratio of white cars to blue cars.
Step 3: Solve the equation.
First, find one-third of 48, which gives you the number of blue cars:
Then find the number of white cars:
white = 48 – (blue + red)
white = 48 – (16 + 24) = 8
Now find the ratio of white cars to blue cars:
8 white:16 blue
8:16
You can further reduce these numbers by 8. The ratio is then 1:2, choice A.
Independent Practice
Turn the page after you solve this item to see our solution.
12. A medical research group is testing a new antibiotic on a random sample of patients. In this sample, 25 patients have some type of food allergies, 15 have lactose intolerance, 8 have both food allergies and lactose intolerance, and 3 have neither. What is the total number of patients in the sample?
Independent Practice: Explanation
Step 1: Determine what the item is really asking you to solve.
This grid-in item asks you to find the total number of patients in a sample that includes two sets: patients with allergies and patients with lactose intolerance. Remember that you also have patients who have both allergies and lactose intolerance, and those who have neither.
Step 2: Create an equation.
To solve this item, recall the formula for the total number of elements, which we introduced in the Essential Concepts section:
Total number = number in set 1 + number in set 2 – intersection of sets 1 and 2 + number in neither set
Total number = patients with food allergies + patients with lactose intolerance – patients with both food allergies and lactose intolerance + healthy patients
Step 3: Solve the equation.
You know the number of patients in set 1 (25) and in set 2 (15). The intersection of the two sets is 8 patients. Don’t forget to add 3 healthy patients as neither.
Total number of patients = 25 + 15 – 8 + 3 = 35. Grid in this number.
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