A. In triangle, the second angle measures twice the first, and the third angle measures 5 more than the second. If the sum of the angles' measures is 180^0, find the measure of each angle.
b. The price of a pack of gum today is 63 cent. This is 3 cent more than three times the price 10 years ago. What was the price 10 years ago?
c. The length of a rectangle is 6 feet more than twice the width. If the length is 24 feet, what is the width?
a. Let's solve this step-by-step:
1. Let's call the first angle x.
2. According to the problem, the second angle measures twice the first, so the second angle measures 2x.
3. The third angle measures 5 more than the second, so the third angle measures 2x + 5.
4. The sum of the angle measures in a triangle is 180°. So we can write the equation as: x + 2x + (2x + 5) = 180.
5. Simplify the equation: 5x + 5 = 180.
6. Subtract 5 from both sides: 5x = 175.
7. Divide both sides by 5: x = 35.
8. Now we can find the measures of the angles:
- The first angle is x = 35°.
- The second angle is 2x = 2(35) = 70°.
- The third angle is 2x + 5 = 2(35) + 5 = 75°.
b. Let's solve this step-by-step:
1. Let's call the price 10 years ago y.
2. According to the problem, the price today is 3 cents more than three times the price 10 years ago. So we can write the equation as: 3y + 3 = 63.
3. Subtract 3 from both sides: 3y = 60.
4. Divide both sides by 3: y = 20.
5. So the price 10 years ago was 20 cents.
c. Let's solve this step-by-step:
1. Let's call the width of the rectangle w.
2. According to the problem, the length is 6 feet more than twice the width, so the length is 2w + 6.
3. According to the problem, the length is 24 feet. So we can write the equation as: 2w + 6 = 24.
4. Subtract 6 from both sides: 2w = 18.
5. Divide both sides by 2: w = 9.
6. So the width of the rectangle is 9 feet.
a. To solve for the angles in a triangle, we can set up equations based on the given information. Let's denote the measure of the first angle as x degrees.
The second angle measures twice the first, so it is 2x degrees.
The third angle measures 5 more than the second, so it is 2x + 5 degrees.
The sum of the angles in a triangle is 180 degrees, so we can write the equation:
x + 2x + (2x + 5) = 180
Combining like terms, we have:
5x + 5 = 180
Subtracting 5 from both sides:
5x = 175
Dividing both sides by 5:
x = 35
So, the first angle measures 35 degrees, the second angle measures 2 * 35 = 70 degrees, and the third angle measures 70 + 5 = 75 degrees.
b. Let's denote the price 10 years ago as x cents.
According to the given information, the price of a pack of gum today is 3 cents more than three times the price 10 years ago, so we can write the equation:
3x + 3 = 63
Subtracting 3 from both sides:
3x = 60
Dividing both sides by 3:
x = 20
Therefore, the price of the pack of gum 10 years ago was 20 cents.
c. Let's denote the width of the rectangle as x feet.
According to the given information, the length of the rectangle is 6 feet more than twice the width, so we can write the equation:
2x + 6 = 24
Subtracting 6 from both sides:
2x = 18
Dividing both sides by 2:
x = 9
Hence, the width of the rectangle is 9 feet.
A. x + 2x + 2x+5 = 180
B. 63 = 3+3x
C. 24 = 6+2x
in each case, solve for x. See how the words have been translated into symbols.