1. The numerator and denominator of a fraction are in the ratio of 3 to 4. If 4 is added to the numerator and subtracted from the denominator, the value of the resulting fraction is 4/3. The numerator of the original fraction is
A. 12
B.
C. 3
D. 4
2. If it takes b hours to walk a certain distance at the rate of 3 miles an hour, the number of hours it takes to return the same distance at 4 miles an hour is
A. 4/3
B. 4b/3
C. 3b/4
D. 3/4
3. The perimeter of a rectangle is 20 inches and its length is 6 inches. The area of the rectangle in square is
A. 20
B. 24
C. 60
D. 48
number 1 choice b is 9
I'll do #1. How about you show some effort on the others? Just write the words in symbols.
If the fraction is n/d, then we are told
n/d = 3/4
(n+4)/(d-4) = 4/3
Work through all that, and you have n=12,d=16
check:
12+4 / 16-4 = 16/12 = 4/3
OK
1. Let's assume the numerator of the original fraction is 3x and the denominator is 4x, where x is a common factor.
According to the given information, if 4 is added to the numerator and subtracted from the denominator, the resulting fraction is 4/3.
So we can set up the equation:
(3x + 4)/(4x - 4) = 4/3
Cross multiplying gives us:
3(3x + 4) = 4(4x - 4)
Expanding both sides gives us:
9x + 12 = 16x - 16
Rearranging the equation gives us:
16x - 9x = 12 + 16
7x = 28
x = 28/7
x = 4
Since the numerator of the original fraction is 3x, substitute x = 4 into the expression:
3(4) = 12
Therefore, the numerator of the original fraction is 12.
The answer is A. 12.
2. The time it takes to walk a certain distance is equal to the distance divided by the rate of walking.
Let's assume the distance is d and the time it takes to walk is b hours.
So, d = 3b.
To find the time it takes to return the same distance at 4 miles an hour, we need to find the distance using the given rate.
The distance can be calculated using the formula: distance = rate * time.
Let's assume the time it takes to return is t hours.
So, d = 4t.
Since the distance remains the same, we can equate the two expressions for d:
3b = 4t
Solving for t gives us:
t = (3/4) * b
Therefore, the number of hours it takes to return the same distance at 4 miles an hour is (3/4) * b.
The answer is C. 3b/4.
3. The perimeter of a rectangle is calculated by adding the lengths of all its sides.
Given that the perimeter is 20 inches and the length is 6 inches, let's assume the width of the rectangle is w inches.
The formula for the perimeter of a rectangle is: perimeter = 2(length + width).
Substituting the given values, we get:
20 = 2(6 + w)
Expanding the expression and solving for w gives us:
20 = 12 + 2w
2w = 8
w = 4
Now that we know the width is 4 inches, we can calculate the area of the rectangle using the formula: area = length * width.
Substituting the values, we get:
area = 6 * 4
area = 24
Therefore, the area of the rectangle in square inches is 24.
The answer is B. 24.
1. To solve this problem, let's assume that the numerator of the original fraction is 3x and the denominator is 4x, where x is some constant. Given that the resulting fraction after adding 4 to the numerator and subtracting it from the denominator is 4/3, we can set up the following equation:
(3x + 4)/(4x - 4) = 4/3
To solve for x, we need to cross-multiply and simplify the equation:
3(3x + 4) = 4(4x - 4)
9x + 12 = 16x - 16
12 + 16 = 16x - 9x
28 = 7x
x = 4
Now that we have the value of x, we can determine the numerator of the original fraction:
Numerator = 3x = 3(4) = 12
Therefore, the correct answer is A. 12.
2. Let's assume that the distance walked is D. We know that the time taken to walk this distance at a rate of 3 miles per hour is b hours. Therefore, the equation we can set up is:
Distance = Rate x Time
D = 3b
To find the number of hours it takes to return the same distance at 4 miles per hour, we need to divide the distance by the rate:
Time = Distance / Rate
Time = D / 4
Substituting the value of D from the equation D = 3b, we get:
Time = (3b) / 4
Therefore, the answer is C. 3b/4.
3. The perimeter of a rectangle is given by the formula: P = 2(length + width)
We are given that the perimeter is 20 inches and the length is 6 inches. Plugging these values into the formula, we get:
20 = 2(6 + width)
Now, we can solve for the width by isolating it on one side of the equation:
20/2 = 6 + width
10 = 6 + width
width = 10 - 6
width = 4 inches
To find the area of the rectangle, we use the formula: Area = length x width
Area = 6 x 4
Area = 24 square inches
Therefore, the correct answer is B. 24.