Set of four math word problems involving real-life scenarios like saving money, calculating averages, and percentages.

Problem 1: Angular's Bike Savings

Question:
Angela is saving money for a new bike. She has $\frac{2}{3}$ of the amount of money she needs for the bike. She has $120 saved. How much does the bike cost? If she saves $10 a week, how many more weeks will it take for her to buy the bike?

Solution:
1. Find the total cost of the bike:
Angela has $\frac{2}{3}$ of the total cost of the bike, which is $120. Let the total cost of the bike be $x$. Then:
\[
\frac{2}{3}x = 120
\]
To find $x$, multiply both sides by $\frac{3}{2}$:
\[
x = 120 \times \frac{3}{2} = 180
\]
So, the total cost of the bike is $180.

2. Calculate the remaining amount needed:
Angela has already saved $120, so the remaining amount she needs is:
\[
180 - 120 = 60
\]

3. Determine the number of weeks needed to save the remaining amount:
Angela saves $10 per week. To find out how many weeks it will take her to save $60, divide the remaining amount by her weekly savings:
\[
\frac{60}{10} = 6
\]
So, it will take her 6 more weeks to save enough money to buy the bike.

Final Answer for Problem 1:
\[
\boxed{180 \text{ dollars}, 6 \text{ weeks}}
\]

---

Problem 2: Average High Temperatures

Question:
The high temperatures for the first five days in December were as follows: $28^\circ$, $31^\circ$, $-2^\circ$, $-4^\circ$, and $12^\circ$. What is the average high temperature of the five days? If the next day's high temperature is $0^\circ$, would the average of the six days increase or decrease?

Solution:
1. Calculate the average high temperature for the first five days:
The temperatures are $28^\circ$, $31^\circ$, $-2^\circ$, $-4^\circ$, and $12^\circ$. First, find the sum of these temperatures:
\[
28 + 31 + (-2) + (-4) + 12 = 28 + 31 - 2 - 4 + 12 = 65
\]
The average temperature for the five days is:
\[
\frac{65}{5} = 13
\]

2. Calculate the average high temperature for six days if the next day's high is $0^\circ$:
Add the next day's temperature ($0^\circ$) to the sum of the first five days:
\[
65 + 0 = 65
\]
The average temperature for the six days is:
\[
\frac{65}{6} \approx 10.83
\]

3. Compare the averages:
The average temperature for the first five days is $13$, and the average temperature for the six days is approximately $10.83$. Since $10.83 < 13$, the average decreases when the next day's temperature is included.

Final Answer for Problem 2:
\[
\boxed{13, \text{decrease}}
\]

---

Problem 3: Math Worksheet Problems

Question:
Your math teacher gives you a worksheet that has 20 problems. She tells you to complete $\frac{3}{4}$ of the problems. If you get one-third of the assigned problems done in class, how many problems do you have for homework?

Solution:
1. Calculate the number of problems assigned:
The teacher asks you to complete $\frac{3}{4}$ of the 20 problems. So, the number of problems assigned is:
\[
\frac{3}{4} \times 20 = 15
\]

2. Calculate the number of problems completed in class:
You complete one-third of the assigned problems in class. So, the number of problems completed in class is:
\[
\frac{1}{3} \times 15 = 5
\]

3. Calculate the number of problems left for homework:
The number of problems left for homework is the total assigned problems minus the problems completed in class:
\[
15 - 5 = 10
\]

Final Answer for Problem 3:
\[
\boxed{10}
\]

---

Problem 4: Jennifer's Savings

Question:
Jennifer has been saving $4.50 a week from her allowance for several weeks. Today she spent $12, which is $\frac{3}{7}$ of her savings. How many weeks has she been saving her money?

Solution:
1. Find Jennifer's total savings before spending:
Jennifer spent $12, which is $\frac{3}{7}$ of her total savings. Let her total savings be $x$. Then:
\[
\frac{3}{7}x = 12
\]
To find $x$, multiply both sides by $\frac{7}{3}$:
\[
x = 12 \times \frac{7}{3} = 28
\]
So, Jennifer's total savings before spending was $28.

2. Calculate the number of weeks Jennifer has been saving:
Jennifer saves $4.50 per week. To find out how many weeks she has been saving, divide her total savings by her weekly savings:
\[
\frac{28}{4.50} = \frac{280}{45} = \frac{56}{9} \approx 6.22
\]
Since the number of weeks must be a whole number, we conclude that Jennifer has been saving for 6 weeks (as she cannot save for a fraction of a week in this context).

Final Answer for Problem 4:
\[
\boxed{6}
\]

---

Final Answers:

1. \(\boxed{180 \text{ dollars}, 6 \text{ weeks}}\)
2. \(\boxed{13, \text{decrease}}\)
3. \(\boxed{10}\)
4. \(\boxed{6}\)