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Example 5

Nick charges $$10$ for each hour of babysitting plus an additional $$7$ for travel costs.

Write an equation to represent the number of dollars, $D$, that Nick charges for $h$ hours of babysitting.
If Nick charges $$62$, how many hours did he babysit?

Solution

Substitute $D=62$ into the equation.
\[\begin{align*} D&=10h+7 \\ \class{timed in4}{62}&\class{timed in4}{\;=10h+7} \\ \class{timed in5}{62 \class{hl2}{-7}} &\class{timed in5}{\;= 10h+7 \class{hl2}{-7}} \\ \class{timed in6}{55} &\class{timed in6}{\;=10h} \\ \class{timed in7}{\dfrac{55}{\class{hl1}{10}}} &\class{timed in7}{\;=\dfrac{10h}{\class{hl1}{10}}} \\ \class{timed in8}{5.5} &\class{timed in8}{\;=h } \end{align*}\]
Verify: We have that $10(5.5)+7=62$. ✔
We conclude that Nick babysat for $5.5$ hours.

Example 6

Janine pays $$35$ each month for a data plan and $$0.40$ for each minute she spends talking on the phone.

Write an equation to represent the monthly cost, $C$, of Janine's cell phone plan if she spends $m$ minutes talking on the phone.
If Janine's cell phone bill was $$51.40$, how many minutes did she spend talking on the phone?

Solution

Substitute $C=51.40$ into the equation.
\[\begin{align*} C &= 0.40m+35 \\ \class{timed in5}{51.40} &\class{timed in5}{\;= 0.40m+35} \\ \class{timed in6}{51.40 \class{hl2}{-35}} &\class{timed in6}{\;= 0.40m+35 \class{hl2}{-35}} \\ \class{timed in7}{16.40} &\class{timed in7}{\;= 0.40m} \\ \class{timed in8}{\dfrac{16.40}{\class{hl1}{0.40}}} &\class{timed in8}{\;=\dfrac{0.40m}{\class{hl1}{0.40}}} \\ \class{timed in9}{41} &\class{timed in9}{\;=m} \end{align*}\]
Verify: We have that $0.40(41)+35=51.40$. ✔
We conclude that Janine spent $41$ minutes talking on her phone.

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