6. a student answers 85% of the questions on a test correctly. the student correctly answers 34 questions. what is the total number of questions on the test? 7. an athlete played in a basketball tournament last year and this year. the athlete scored 15 points last year. the athlete scored 25 points this year. what is the percent of change in points from last year to this year? round to the nearest whole percent. 8. a person invests $600 in an account that earns 3% simple interest. how much interest is earned in 1 year? 9. a person buys a meal and tips 20%. select all the meals the person could buy for a total of $15 or less. a. $10.00 meal b. $11.75 meal c. $12.50 meal d. $13.25 meal e. $15.00 meal 10. a family of five goes to dinner. - the food costs $122.35. - the family gave the server a 20% tip before tax was applied. - there is a 6.5% sales tax on the food only. what is the total cost of the meal? 11. a shirt is on sale. - the original price of the shirt is $11.50. - the sale price of the shirt is $10.12. what percent discount did the store apply to the shirt?

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Accepted Answer

### Question 6
# Explanation:
## Step1: Define the relationship
Let $ x $ be the total number of questions. We know that $ 85\% $ of $ x $ is equal to 34. Mathematically, this is $ 0.85x = 34 $.
## Step2: Solve for $ x $
To find $ x $, we divide both sides of the equation by $ 0.85 $: $ x=\frac{34}{0.85} $.
Calculating $ \frac{34}{0.85}=40 $.
# Answer:
The total number of questions on the test is 40.

### Question 7
# Explanation:
## Step1: Recall the percent change formula
The formula for percent change is $ \text{Percent Change}=\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times 100\% $.
## Step2: Identify values
The old value (last year's points) is 15, and the new value (this year's points) is 25.
## Step3: Substitute into the formula
First, calculate the difference: $ 25 - 15 = 10 $. Then, $ \text{Percent Change}=\frac{10}{15}\times 100\% \approx 66.67\% $, which rounds to 67%.
# Answer:
The percent of change in points is approximately 67%.

### Question 8
# Explanation:
## Step1: Recall the simple interest formula
The formula for simple interest is $ I = Prt $, where $ P $ is the principal amount, $ r $ is the annual interest rate (in decimal), and $ t $ is the time in years.
## Step2: Identify values
Here, $ P = 600 $, $ r = 0.03 $ (since $ 3\%=0.03 $), and $ t = 1 $.
## Step3: Substitute into the formula
$ I=600\times0.03\times 1 = 18 $.
# Answer:
The interest earned in 1 year is $18.

### Question 9
# Explanation:
## Step1: Define the total cost formula
If the meal cost is $ m $, the total cost (meal + tip) is $ m + 0.20m=1.20m $. We want $ 1.20m\leq15 $.
## Step2: Solve for $ m $
Divide both sides by 1.20: $ m\leq\frac{15}{1.20}=12.5 $.
## Step3: Check each option
- a. $ m = 10.00 $: $ 1.20\times10 = 12\leq15 $ (valid)
- b. $ m = 11.75 $: $ 1.20\times11.75 = 14.1\leq15 $ (valid)
- c. $ m = 12.50 $: $ 1.20\times12.50 = 15\leq15 $ (valid)
- d. $ m = 13.25 $: $ 1.20\times13.25 = 15.9>15 $ (invalid)
- e. $ m = 15.00 $: $ 1.20\times15 = 18>15 $ (invalid)
# Answer:
The meals the person could buy are a. $10.00 meal, b. $11.75 meal, c. $12.50 meal.

### Question 10
# Explanation:
## Step1: Calculate the tip amount
The tip is 20% of the food cost. The food cost is $122.35, so the tip $ T = 0.20\times122.35 = 24.47 $.
## Step2: Calculate the tax amount
The tax is 6.5% of the food cost. So, $ \text{Tax}=0.065\times122.35\approx7.95275 $.
## Step3: Calculate the total cost
Total cost = Food cost + Tip + Tax. So, $ 122.35+24.47 + 7.95275=154.77275\approx154.77 $.
# Answer:
The total cost of the meal is approximately $154.77.

### Question 11
# Explanation:
## Step1: Recall the discount formula
Let $ d $ be the discount rate (in decimal). The sale price $ S = \text{Original Price}(1 - d) $.
## Step2: Identify values
Original price $ P = 11.50 $, sale price $ S = 10.12 $.
## Step3: Substitute into the formula
$ 10.12=11.50(1 - d) $. First, divide both sides by 11.50: $ \frac{10.12}{11.50}=1 - d $.
Calculating $ \frac{10.12}{11.50}=0.879\approx0.88 $. Then, $ 0.88 = 1 - d $, so $ d = 1 - 0.88 = 0.12 $, which is 12%.
# Answer:
The store applied a 12% discount to the shirt.

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QUESTION IMAGE

Question

Explanation:

Question 6

Step1: Define the relationship

Step2: Solve for \( x \)

Step1: Recall the percent change formula

Step2: Identify values

Step3: Substitute into the formula

Step1: Recall the simple interest formula

Step2: Identify values

Step3: Substitute into the formula

Answer:

Question 7