Solve the folowing:
1. One number si les than another number. if the sum of the two numbers are 177, find each number.
2.Find 45% of 125.
3.Find the measure of each angle in the figure below. Note that since the angles make up a straight line, they are supplementary to each other.
4.The sum of a number and 2 is 6 less than twice that number. 
5. Find 72% of 35.
6. A math class has 30 students. Approximately 70% passed their last math test. How many students passed the last math test?
7.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 solve each of the problems one by one:

---

### 1. **One number is less than another number. If the sum of the two numbers is 177, find each number.**

Let the two numbers be \( x \) and \( y \), where \( x \) is the smaller number and \( y \) is the larger number. The relationship can be expressed as:
- \( y = x + 1 \) (since one number is 1 more than the other).
- The sum of the numbers is \( x + y = 177 \).

Substituting \( y = x + 1 \) into the sum equation:
\[
x + (x + 1) = 177
\]
\[
2x + 1 = 177
\]
\[
2x = 176
\]
\[
x = 88
\]

Now, substitute \( x = 88 \) into \( y = x + 1 \):
\[
y = 88 + 1 = 89
\]

**Answer**: The two numbers are \( 88 \) and \( 89 \).

---

### 2. **Find 45% of 125.**

To find 45% of 125, use the formula:
\[
\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total value}
\]
\[
\text{Percentage value} = \frac{45}{100} \times 125 = 0.45 \times 125 = 56.25
\]

**Answer**: 45% of 125 is 56.25.

---

### 3. **Find the measure of each angle in the figure below. The angles make up a straight line and are supplementary to each other.**

For supplementary angles, the sum is 180°.

Let the two angles be \( x \) and \( y \). Since they are supplementary:
\[
x + y = 180^\circ
\]
Without the exact figure, I can assume you need the general formula. If you know one angle, subtract it from 180° to find the other angle.

For example, if one angle is given as \( x \), the other is \( 180^\circ - x \).

---

### 4. **The sum of a number and 2 is 6 less than twice that number.**

Let the number be \( x \). The equation can be written as:
\[
x + 2 = 2x - 6
\]

Solve for \( x \):
\[
x + 2 = 2x - 6
\]
\[
2 + 6 = 2x - x
\]
\[
x = 8
\]

**Answer**: The number is \( 8 \).

---

### 5. **Find 72% of 35.**

To find 72% of 35, use the formula:
\[
\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total value}
\]
\[
\text{Percentage value} = \frac{72}{100} \times 35 = 0.72 \times 35 = 25.2
\]

**Answer**: 72% of 35 is 25.2.

---

### 6. **A math class has 30 students. Approximately 70% passed their last math test. How many students passed the last math test?**

To find 70% of 30:
\[
\text{Number of students passed} = \frac{70}{100} \times 30 = 0.70 \times 30 = 21
\]

**Answer**: 21 students passed the test.

---

### 7. **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 the length of the garden be \( L \) and the width be \( W \). From the problem, we know:
\[
W = 2L - 8
\]
The perimeter of a rectangle is given by:
\[
P = 2L + 2W = 20
\]

Substitute \( W = 2L - 8 \) into the perimeter equation:
\[
2L + 2(2L - 8) = 20
\]
\[
2L + 4L - 16 = 20
\]
\[
6L - 16 = 20
\]
\[
6L = 36
\]
\[
L = 6
\]

Now substitute \( L = 6 \) into \( W = 2L - 8 \):
\[
W = 2(6) - 8 = 12 - 8 = 4
\]

**Answer**: The dimensions of the garden are 6 feet by 4 feet.

---

Let me know if you'd like more details! Here are five related questions for further practice:

1. Solve for two numbers where one is 5 less than the other, and their sum is 130.
2. Find 55% of 220.
3. If three angles form a straight line, and two angles are known, how do you find the third angle?
4. The sum of a number and 4 is 8 less than three times that number. What is the number?
5. Find 65% of 50.

**Tip**: To solve percentage problems faster, you can convert the percentage to a decimal and multiply it by the total value.

1. One number is less than another number. If the sum of the two numbers is 177, find each number.
2. Find 45% of 125.
3. Find the measure of each angle in the figure below. Note that since the angles make up a straight line, they are supplementary to each other.
4. The sum of a number and 2 is 6 less than twice that number.
5. Find 72% of 35.
6. A math class has 30 students. Approximately 70% passed their last math test. How many students passed the last math test?
7. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.

This page provides step-by-step solutions to common middle school math problems, including algebraic equations, percentage calculations, and geometry involving supplementary angles and perimeter. Learn how to find unknown numbers, calculate percentages, and solve linear equations with clear examples.

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