Math Problem Statement

julia took a 20-item math test. if she got 14 out of 20 items correctly, what is her grade in perfect? if she got 85% in the test, how many times did the she got wrong? with solution

Solution

Let's solve this step by step:

Part 1: Calculating Julia's Grade in Percent

Julia answered 14 out of 20 items correctly. To find her grade in percent, we use the formula:

Grade (%)=(Number of Correct AnswersTotal Number of Questions)×100\text{Grade (\%)} = \left(\frac{\text{Number of Correct Answers}}{\text{Total Number of Questions}}\right) \times 100

Substituting the values:

Grade (%)=(1420)×100=70%\text{Grade (\%)} = \left(\frac{14}{20}\right) \times 100 = 70\%

So, Julia's grade is 70%.

Part 2: Finding the Number of Wrong Answers if She Got 85%

If Julia got 85% in the test, we can use the percent to find out how many items she got right and then subtract that number from the total to find how many she got wrong.

  1. Let xx be the number of correct answers if her score was 85%.

Using the percentage formula:

Correct Answers=Percent Score100×Total Number of Questions\text{Correct Answers} = \frac{\text{Percent Score}}{100} \times \text{Total Number of Questions}

Substituting the values:

x=85100×20=17x = \frac{85}{100} \times 20 = 17

So, she got 17 items correct.

  1. To find the number of wrong answers:

Wrong Answers=Total Number of QuestionsCorrect Answers=2017=3\text{Wrong Answers} = \text{Total Number of Questions} - \text{Correct Answers} = 20 - 17 = 3

Therefore, if Julia got 85% on the test, she got 3 items wrong.


Do you want more details or have any questions?

Here are some related questions:

  1. If Julia had answered 18 items correctly, what would her grade be in percent?
  2. How many items did she need to answer correctly to achieve a score of 90%?
  3. If Julia's goal was to score at least 75%, how many items did she need to answer correctly?
  4. What percentage would Julia get if she answered 10 items correctly?
  5. If Julia's grade increased by 10%, how many additional items did she need to answer correctly?

Tip: Always double-check your calculations, especially when converting between percentages and actual counts!

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Math Problem Analysis

Mathematical Concepts

Percentages
Basic Arithmetic

Formulas

Grade (%) = (Number of Correct Answers / Total Number of Questions) * 100
Correct Answers = (Percent Score / 100) * Total Number of Questions
Wrong Answers = Total Number of Questions - Correct Answers

Theorems

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Suitable Grade Level

Grades 5-7