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Janie has $\$3$ . She earns $\$1.20$ for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $\$13.50$ Write an inequality to determine the number of chores, $c$ , Janie could do to have enough money to buy the CD.

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One-step inequalities: word problems

Full solution

Q. Janie has

\$3

. She earns

\$1.20

for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for

\$13.50

Write an inequality to determine the number of chores,

c

, Janie could do to have enough money to buy the CD.

Set Up Inequality: Janie starts with $\$3$ and wants to buy a CD for $\$13.50$ . She earns $\$1.20$ per chore. We need to set up an inequality to find the minimum number of chores, $c$ , she needs to do to have at least $\$13.50$ . The inequality will be in the form of her initial amount plus the amount she earns per chore times the number of chores being greater than or equal to the cost of the CD. So, the inequality is: $3 + 1.20c \geq 13.50$
Subtract to Isolate: Subtract $\$3$ from both sides of the inequality to isolate the term with $c$ on one side. $\newline$ $3 + 1.20c - 3 \geq 13.50 - 3$ $\newline$ This simplifies to: $\newline$ $1.20c \geq 10.50$
Divide to Solve: Divide both sides of the inequality by $1.20$ to solve for $c$ . $\newline$ $\frac{1.20c}{1.20} \geq \frac{10.50}{1.20}$ $\newline$ This simplifies to: $\newline$ $c \geq 8.75$

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