Let's solve each of the problems one by one:

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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 $89$.

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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.

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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 $180^\circ - x$.

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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 $8$.

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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.

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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.

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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.

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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.