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Miyoko's goal is to earn more than
$950 this week. She earns
$250 for every day she works as a cryptographer, and earns
$180 for every day she works as a geologist.
Write an inequality that represents the number of days Miyoko should work as a cryptographer
(C) and as a geologist
(G) to achieve her goal.

Miyoko's goal is to earn more than $(950$ this week. She earns $)250$ for every day she works as a cryptographer, and earns $\$180$ for every day she works as a geologist. $\newline$ Write an inequality that represents the number of days Miyoko should work as a cryptographer $C$ and as a geologist $G$ to achieve her goal.

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Modeling with linear inequalities

Full solution

Q. Miyoko's goal is to earn more than

(950

this week. She earns

)250

for every day she works as a cryptographer, and earns

\$180

for every day she works as a geologist.

\newline

Write an inequality that represents the number of days Miyoko should work as a cryptographer

C

and as a geologist

G

to achieve her goal.

Identify daily earnings: Identify the daily earnings for each job. $\newline$ Miyoko earns $\$250$ for every day she works as a cryptographer and $\$180$ for every day she works as a geologist.
Set up inequality for total earnings: Set up the inequality to represent the total earnings from both jobs. $\newline$ The total earnings from working as a cryptographer for $C$ days is $250C$ , and the total earnings from working as a geologist for $G$ days is $180G$ . Miyoko's goal is to earn more than $\$950$ , so we can write the inequality as $250C + 180G > 950$ .
Check inequality for accuracy: Check the inequality to ensure it represents the situation correctly. $\newline$ Miyoko wants to earn more than $\$950$ , so the inequality symbol should be '>'. The coefficients $250$ and $180$ correctly represent her daily earnings for each job, and the sum of these earnings should be greater than $\$950$ .

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