Certainly! Let's break down the solution to find out how many total points the test was worth.
The information provided tells us that the student scored 90% on the test and earned 70 points. We need to determine the total possible points the test was worth.
### Step-by-Step Solution:
1. Understand the Given Information:
- The student scored 90% on the test.
- She earned 70 points.
2. Set Up the Relationship:
The score percentage can be expressed as:
[tex]\[
\text{Percentage Score} = \left(\frac{\text{Points Earned}}{\text{Total Points}}\right) \times 100\%
\][/tex]
We are given:
[tex]\[
90\% = \left(\frac{70}{\text{Total Points}}\right) \times 100\%
\][/tex]
3. Convert the Percentage to a Decimal:
90% can be written as 0.90.
4. Formulate the Equation:
We can now set up the equation with the decimal form:
[tex]\[
0.90 = \frac{70}{\text{Total Points}}
\][/tex]
5. Solve for Total Points:
Rearrange the equation to solve for the total points:
[tex]\[
\text{Total Points} = \frac{70}{0.90}
\][/tex]
6. Calculate the Total Points:
Performing the division gives:
[tex]\[
\text{Total Points} ≈ 77.77777777777777
\][/tex]
7. Round to the Nearest Whole Number:
The next step is to round the result to the nearest whole number. Rounding 77.77777777777777 gives us:
[tex]\[
\text{Total Points} ≈ 78
\][/tex]
### Final Answer:
The total points the test was worth, rounded to the nearest point, is 78 points.
