1) If A is 125% of B, then B is what percent of A?
A) 60%
B) 75%
C) 80%
D) 88%
E) 90%
2) In an opinion poll of 50 men and 40 women, 70% of the men and 25% of the women said that they preferred fiction to nonfiction books. What percent of the number of people polled preferred to red fiction?
a) 40%
b) 45%
c) 50%
d) 60%
e) 75%
3) A number a increased by 20% of a results in a number b. When b is decreased by 33 1/3% of b, the result is c. The number c is what percent of a?
a) 40%
b) 60%
c) 80%
d) 120%
e) 150%
What choices did you pick?
Where are your difficulties?
I will do the first one, you try the others
If A is 125% of B ----> A = 1.25B
B = (1/1.25)A
= .8A
so B is 80% of A
1)a
2)b
1) If A is 125% of B, then B is what percent of A?
To find the percentage of B in relation to A, we can use the reciprocal of the given percentage, which is 1/1.25 or 0.8. Therefore, B is 80% of A.
The answer is C) 80%.
2) In an opinion poll of 50 men and 40 women, 70% of the men and 25% of the women said that they preferred fiction to nonfiction books. What percent of the number of people polled preferred to read fiction?
To find the total number of people who prefer fiction, we need to calculate the number of men who prefer fiction and the number of women who prefer fiction, then add them together.
The number of men who prefer fiction is 70% of 50, which is 0.7 * 50 = 35.
The number of women who prefer fiction is 25% of 40, which is 0.25 * 40 = 10.
Now, we add these two numbers together: 35 + 10 = 45.
Since we are looking for the percentage of people who prefer fiction out of the total number polled, which is 90 (50 men + 40 women), we divide the number of people who prefer fiction (45) by the total number (90) and multiply by 100.
(45/90) * 100 = 50
The answer is C) 50%.
3) A number a increased by 20% of a results in a number b. When b is decreased by 33 1/3% of b, the result is c. The number c is what percent of a?
Let's break it down step by step:
Step 1: "A number a increased by 20% of a results in a number b."
This can be represented as a + (20% of a) = b, which simplifies to a + 0.2a = b, or 1.2a = b.
Step 2: "When b is decreased by 33 1/3% of b, the result is c."
This can be represented as b - (33 1/3% of b) = c, which simplifies to b - 0.3333b = c, or 0.6667b = c.
Step 3: In terms of a, we can substitute b with 1.2a from Step 1:
0.6667 * 1.2a = c
Simplifying the equation gives us 0.8a = c.
Step 4: To find the percentage of c in relation to a, we can divide c by a and multiply by 100:
(c/a) * 100 = (0.8a/a) * 100 = 0.8 * 100 = 80.
The answer is C) 80%.
1) To determine what percent B is of A, we can set up the following proportion:
A is 125% of B, so A = 1.25B.
To find B as a percentage of A, we can rewrite the equation as B = A/1.25.
Now, we can substitute the values of the answer choices into the equation to solve for B and find the correct percentage.
Let's try option A: B = A/1.25 = 1/1.25 = 0.8 = 80%.
B is 80% of A, so the correct answer is option C) 80%.
2) We have the following information from the opinion poll:
70% of the 50 men preferred fiction = (70/100) * 50 = 35 men.
25% of the 40 women preferred fiction = (25/100) * 40 = 10 women.
So, the total number of people who preferred fiction is 35 + 10 = 45.
We are asked to find the percentage of people who preferred fiction out of the total number of people polled (50 men + 40 women = 90 people).
The percentage is (45/90) * 100 = 50%.
Therefore, the correct answer is option C) 50%.
3) We start with the information that number a increased by 20% results in number b.
Mathematically, this can be written as b = a + (20/100) * a = a(1 + 0.2) = 1.2a.
Next, we are told that when b is decreased by 33 1/3% of b, the result is c.
Mathematically, this can be expressed as c = b - (33 1/3/100) * b = b(1 - 0.3333) = 0.6667b.
We are asked to find c as a percentage of a, which means c/a * 100.
Substituting the values, we have (0.6667b/a) * 100 = (0.6667 * 1.2a/a) * 100 = 0.8 * 100 = 80%.
Therefore, the correct answer is option C) 80%.