1. The sum of a number and 2 is 6 less than twice that number.
2. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.
3. Complementary angles sum up to equal 90 degrees. Find the measure of each angle in the figure below. Note that since the angles make up a right angle, they are complementary to each other.
angle #1 = x = ?
angle #2 = X + 30 = ?
4. Six times a number is less than 72. What numbers satisfy this condition?
5. A number increased by 10 is greater than 50. What numbers satisfy this condition?
6. A number decreased by 15 is less than 35. What numbers satisfy this condition?
7. Twice a number, increased by 6, is less than 48. What numbers satisfy this condition?
8. Five times a number, decreased by 24, is greater than 3 times the number. What numbers satisfy this condition?
9. Five times the difference of a number and two is seven more than that number.
10. Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
11. Twice a number decreased by two is equivalent to than number increased by five.
12. One number is five more than another number and the sum of the two numbers is 55, what are the numbers?
13. If you have a rectangular rug whose perimeter is 26 feet and the length is three feet more than the width, what are the dimensions of the rug? (P=2w+2l)
14. If two angles are supplementary (sum of the two angles equals 180 degrees), find each angle if one angle is 30 degrees more than twice the other angle.
Can someone please help out I cant understand how to make them into equations? Maybe please just explain how to. Greatly thanks.
1. Let's call the number "x". The sum of the number and 2 is 6 less than twice that number, which can be written as: x + 2 = 2x - 6.
2. Let's call the length of the rectangular garden "l" and the width "w". The problem states that the width is 8 feet less than twice the length, so we can write: w = 2l - 8. The perimeter of a rectangle is given by the formula P = 2w + 2l, where P is the perimeter. The problem states that the perimeter is 20 feet, so we can write: 20 = 2w + 2l.
3. Since the angles make up a right angle and complementary angles sum up to 90 degrees, we can write: x + (x + 30) = 90.
4. Let's call the number "n". The problem states that six times the number is less than 72, so we can write: 6n < 72.
5. Let's call the number "n". The problem states that a number increased by 10 is greater than 50, so we can write: n + 10 > 50.
6. Let's call the number "n". The problem states that a number decreased by 15 is less than 35, so we can write: n - 15 < 35.
7. Let's call the number "n". The problem states that twice the number, increased by 6, is less than 48, so we can write: 2n + 6 < 48.
8. Let's call the number "n". The problem states that five times the number, decreased by 24, is greater than 3 times the number, so we can write: 5n - 24 > 3n.
9. Let's call the number "n". The problem states that five times the difference of a number and two is seven more than that number, so we can write: 5(n - 2) = n + 7.
10. Let's call the number "n". The problem states that twice the number, decreased by four, is greater than ten, so we can write: 2n - 4 > 10.
11. Let's call the number "n". The problem states that twice the number, decreased by two, is equivalent to the number increased by five, so we can write: 2n - 2 = n + 5.
12. Let's call one number "x" and the other number "y". The problem states that one number is five more than another number, so we can write: x = y + 5. The problem also states that the sum of the two numbers is 55, so we can write: x + y = 55.
13. Let's call the width of the rectangle "w" and the length "l". The problem states that the length is three feet more than the width, so we can write: l = w + 3. The perimeter of a rectangle is given by the formula P = 2w + 2l, where P is the perimeter. The problem states that the perimeter is 26 feet, so we can write: 26 = 2w + 2l.
14. Let's call one angle "x" and the other angle "y". The problem states that one angle is 30 degrees more than twice the other angle, so we can write: x = 2y + 30. Since the angles are supplementary, we can also write: x + y = 180.
Sure, I can help explain how to translate these statements into equations. Let's go through each problem step by step:
1. The sum of a number and 2 is 6 less than twice that number.
Let's assign a variable to the number, such as "x".
The sum of a number (x) and 2 can be represented as: x + 2.
"6 less than twice that number" can be represented as: 2x - 6.
Putting it all together, we get the equation: x + 2 = 2x -6.
2. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.
Let's assign variables to the dimensions of the garden, such as "length" and "width".
The width is 8 feet less than twice the length, so we can represent it as: 2(length) - 8.
The perimeter of a rectangle can be calculated as: 2(length + width).
Since the perimeter is 20 feet, we have the equation: 2(length + (2(length) - 8)) = 20.
3. In the figure, two angles are complementary and sum up to equal 90 degrees.
Let's assign variables to the angles, such as "angle 1" and "angle 2".
The measure of angle 1 can be represented as: x.
"Angle 2 is x + 30" implies that the measure of angle 2 is x + 30.
Since the sum of two complementary angles is 90 degrees, we have the equation: x + (x + 30) = 90.
4. Six times a number is less than 72. What numbers satisfy this condition?
Let's assign a variable to the number, such as "x".
"Six times a number" can be represented as: 6x.
"Is less than 72" can be represented as: 6x < 72.
For the remaining problems, I will provide you with the equations directly:
5. A number increased by 10 is greater than 50: x + 10 > 50.
6. A number decreased by 15 is less than 35: x - 15 < 35.
7. Twice a number, increased by 6, is less than 48: 2x + 6 < 48.
8. Five times a number, decreased by 24, is greater than 3 times the number: 5x - 24 > 3x.
9. Five times the difference of a number and two is seven more than that number: 5(x - 2) = x + 7.
10. Twice a number decreased by four is greater than ten: 2x - 4 > 10.
11. Twice a number decreased by two is equivalent to the number increased by five: 2x - 2 = x + 5.
12. One number is five more than another number and the sum of the two numbers is 55: x = y + 5, x + y = 55.
13. The length of a rectangle is three feet more than the width, and the perimeter is 26 feet: 2(width + (width + 3)) = 26.
14. Two angles are supplementary, with one angle being 30 degrees more than twice the other angle: x + (2x + 30) = 180.
These equations should help you set up and solve the problems. If you need further assistance with solving any of them, feel free to ask!
Sure! I'd be happy to help you understand how to turn these problems into equations.
To solve these problems, we first need to define variables to represent the unknowns in the problem. Let's use the following notation:
- "x" will represent a number.
- "l" will represent the length of a rectangle.
- "w" will represent the width of a rectangle.
- "angle #1" and "angle #2" will represent the measures of two angles.
Now, let's go through each problem and turn them into equations:
1. The sum of a number and 2 is 6 less than twice that number.
Equation: x + 2 = 2x - 6
2. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.
Equation: 2l + 2w = 20
3. Complementary angles sum up to equal 90 degrees. Find the measure of each angle.
Equations:
- angle #1: x
- angle #2: x + 30
x + (x + 30) = 90
4. Six times a number is less than 72. What numbers satisfy this condition?
Equation: 6x < 72
5. A number increased by 10 is greater than 50. What numbers satisfy this condition?
Equation: x + 10 > 50
6. A number decreased by 15 is less than 35. What numbers satisfy this condition?
Equation: x - 15 < 35
7. Twice a number, increased by 6, is less than 48. What numbers satisfy this condition?
Equation: 2x + 6 < 48
8. Five times a number, decreased by 24, is greater than 3 times the number. What numbers satisfy this condition?
Equation: 5x - 24 > 3x
9. Five times the difference of a number and two is seven more than that number.
Equation: 5(x - 2) = x + 7
10. Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
Equation: 2x - 4 > 10
11. Twice a number decreased by two is equivalent to that number increased by five.
Equation: 2x - 2 = x + 5
12. One number is five more than another number and the sum of the two numbers is 55, what are the numbers?
Equations:
- First number: x
- Second number: x + 5
x + (x + 5) = 55
13. If you have a rectangular rug whose perimeter is 26 feet and the length is three feet more than the width, what are the dimensions of the rug? (P=2w+2l)
Equations:
- Perimeter: 2w + 2l = 26
- Length: l = w + 3
14. If two angles are supplementary (sum of the two angles equals 180 degrees), find each angle if one angle is 30 degrees more than twice the other angle.
Equations:
- Angle #1: x
- Angle #2: 2x + 30
x + (2x + 30) = 180
I hope this breakdown of each problem helps you understand how to form the equations. Feel free to ask if you have any more questions!
They are all pretty much the same
I will do a couple
13. If you have a rectangular rug whose perimeter is 26 feet and the length is three feet more than the width, what are the dimensions of the rug? (P=2w+2l)
yes
p = 2 w + 2 l = 26
and
l = w +3
so use (substitute) w+3 for l in the perimeter
2 w + 2 (w+3) = 26
4 w + 6 = 26
4 w = 20
w = 5
so l = 8
the end
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14. If two angles are supplementary (sum of the two angles equals 180 degrees), find each angle if one angle is 30 degrees more than twice the other angle.
A + B = 180
B = 2 A + 30
so just like the rug, use 2 A + 30 for B in the first equation
A + 2 A + 30 = 180
3 A = 150
A = 50
then B = 2 * 50 + 30 = 130