Question: 1. A certain type of vinegar contains 4% acetic acid, so a 16 oz bottle of the vinegar contains 0.64 ounces of acetic acid.
2. A painter paints a wall in x hours, so the fraction of the wall that she paints in 4 hours is 4/x.
3. A cell phone company charges a monthly fee of $30 for the first 1000 text messages and 10 cents for each additional text message. Miriam’s bill for text messages for the month of June is $35.70. How many text messages did she send that month?
1026 text messages
4. In a class of 25 students, the average score is 81. Nine students in the class each received a maximum score of 100, and six students each received a score of 60. What is the average score of the remaining students?
78.5
5. What annual rate of interest would you have to earn on an investment of $2500 to ensure receiving $157.50 interest after 1 year?
6.85%
6. A woman earns 12% more than her husband. Together they make $81,620 per year. What is the husband’s annual salary?
$ 36500
7. A plumber and his assistant work together to replace the pipes in an old house. The plumber charges $40 an hour for his own labor and $20 an hour for his assistant’s labor. The plumber works twice as long as his assistant on this job, and the labor cost is ? The plumber and his assistant work on this job?
plumber 23 h
assistant 11.5 h
1. **Problem:** A cell phone company charges a monthly fee of $30 for the first 1000 text messages and 10 cents for each additional text message. Miriam’s bill for June is $35.70. How many text messages did she send?
2. **Formula:** Total bill = Base fee + (Cost per additional message) \times (Number of additional messages)
3. **Step 1:** Let $x$ be the total number of text messages sent.
4. **Step 2:** Since the first 1000 messages cost $30, additional messages are $x - 1000$.
5. **Step 3:** The cost for additional messages is $0.10 \times (x - 1000)$.
6. **Step 4:** Total bill equation:
$$30 + 0.10(x - 1000) = 35.70$$
7. **Step 5:** Subtract 30 from both sides:
$$0.10(x - 1000) = 35.70 - 30$$
$$0.10(x - 1000) = 5.70$$
8. **Step 6:** Divide both sides by 0.10:
$$\cancel{0.10}(x - 1000) / \cancel{0.10} = 5.70 / 0.10$$
$$x - 1000 = 57$$
9. **Step 7:** Add 1000 to both sides:
$$x = 57 + 1000 = 1057$$
10. **Step 8:** Miriam sent $1057$ text messages.
**Final answer:** $1057$ text messages.