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Precalculus
Solve a system of equations using substitution
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Ernest is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of
$
99
\$99
$99
. Ernest will be earning a base salary of
$
91
\$91
$91
per month from the gym, plus an additional
$
4
\$4
$4
for every class he teaches. If Ernest teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take? How much will Ernest's expenses and earnings be?
\newline
Once Ernest teaches _____ classes, his expenses and earnings will both be
$
\$
$
_____.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Lola just became a personal trainer and is finalizing her pricing plans. One plan is to charge
$
17
\$17
$17
for the initial consultation and then
$
38
\$38
$38
per session. Another plan is to charge
$
19
\$19
$19
for the consultation and
$
36
\$36
$36
per session. Lola realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?
\newline
For _____ sessions, the cost is
$
\$
$
_____ on either plan.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Melissa is going to hire a makeup artist for a fashion show and is comparing prices. Sanjay charges
$
92
\$92
$92
as a booking fee and an additional
$
53
\$53
$53
per hour. Denise charges
$
52
\$52
$52
per hour, plus a booking fee of
$
95
\$95
$95
. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?
\newline
If the show lasted for _____ hours, the cost would always be
$
\$
$
_____.
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Solve the system by substitution.
\newline
y
=
−
x
+
36
y
=
3
x
\begin{array}{l} y=-x+36 \\ y=3 x \end{array}
y
=
−
x
+
36
y
=
3
x
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
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