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19 days ago

14

Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she s

cored 58 points, then she scores 63 and 68 on her next two assessments. If her scores continued to increase at the same rate, on which assessments will she be scoring above 85?

2 answers:

lawyer [9.2K]19 days ago

4 0

This pattern shows an addition of five points for each subsequent assessment.
1st= 58, 2nd=63, 3rd=68, 4th=73, 5th=78, 6th=83, 7th=88 points.
Thus, at her seventh assessment, she'll surpass the 85-point mark.
I hope this clarifies things.

PIT_PIT [9.1K]19 days ago

3 0

Response

After her seventh assessment, she will score above 85.

Explanation

We can represent this situation through a linear equation.

On her initial assessment, Rita scored 58, providing the first point (1, 58).

On her second assessment, Rita earned 63, making our second point (2, 63).

To calculate the rate, known as the slope of our line, we utilize the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where

$(x_{1},y_{1})$ signifies the coordinates for the first point

and $(x_{2},y_{2})$ represents the coordinates for the second point.

From these points, we can establish that $x_{1}=1$ , $y_{1}=58$ , $x_{2}=2$ , $y_{2}=63$ . We will input the values into our slope equation:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{63-58}{2-1}$

$m=\frac{5}{1}$

$m=5$

Now, we recognize that Rita's score grows by 5 points with every assessment.

To finalize the equation of our line, we apply the point-slope formula:

$y-y_{1}=m(x-x_{1})$

$y-58=5(x-1)$

$y-58=5x-5$

$y=5x+53$

Ultimately, we substitute $y$ with 85 in our equation and solve for $x$ to determine on which assessment she will achieve a score higher than 85:

$85=5x+53$

$32=5x$

$x=\frac{32}{5}$

$x=6.4$

Since a score of 0.4 assessments is not possible, she will exceed 85 after her seventh assessment.

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