Given:
Number of new words to learn everyday = 2
Number of words he can spell already = 10
Let's write an inequality to determine the number of whole days it will take for him to be able to spell at least 75 words.
Apply the slope intercept form:
y = mx + b
Where m is the rate of change and b is the initial value.
We have the inequality:
[tex]75\leq2x+10[/tex]
Where:
Initial value = 10
Rate of change = 2
Let's solve for x.
Subtract 10 from both sides:
[tex]\begin{gathered} 75-10\leq2x+10-10 \\ \\ 65\leq2x \end{gathered}[/tex]
Divide both sides by 2:
[tex]\begin{gathered} \frac{65}{2}\leq\frac{2x}{2} \\ \\ 32.5\leq x \\ \\ x\ge32.5\approx33 \end{gathered}[/tex]
Therefore, it will take him aa minimum of 33 days to be able to spell at least 75 words.
ANSWER:
33 days
