the equation ( 9(u - 2)+1.5u = 8.25 ) models the total miles michael traveled one afternoon while sledding…

the equation ( 9(u - 2)+1.5u = 8.25 ) models the total miles michael traveled one afternoon while sledding, where ( u ) equals the number of hours walking up a hill and ( (u - 2) ) equals the number of hours sledding down the hill. which is the value of ( u )?\n( u = 0.25 )\n( u = 0.75 )\n( u = 1.1 )\n( u = 2.5 )

the equation ( 9(u - 2)+1.5u = 8.25 ) models the total miles michael traveled one afternoon while sledding, where ( u ) equals the number of hours walking up a hill and ( (u - 2) ) equals the number of hours sledding down the hill. which is the value of ( u )?\n( u = 0.25 )\n( u = 0.75 )\n( u = 1.1 )\n( u = 2.5 )

Answer

Explanation:

Step1: Expand the equation

$$ \begin{align*} 9(u - 2)+1.5u&=8.25\ 9u-18 + 1.5u&=8.25 \end{align*} $$

Step2: Combine like - terms

$$ \begin{align*} (9u+1.5u)-18&=8.25\ 10.5u-18&=8.25 \end{align*} $$

Step3: Isolate the term with (u)

$$ \begin{align*} 10.5u&=8.25 + 18\ 10.5u&=26.25 \end{align*} $$

Step4: Solve for (u)

$$ u=\frac{26.25}{10.5}=2.5 $$

Answer:

(u = 2.5) (the fourth option)