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Tatiana wants to give friendship bracelets to her classmates. She already has $5$ bracelets, and she can buy more bracelets in packages of $4$ . Write an inequality to determine the number of packages, $p$ , Tatiana could buy to have enough bracelets.

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Write a linear function: word problems

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Q. Tatiana wants to give friendship bracelets to her classmates. She already has

5

bracelets, and she can buy more bracelets in packages of

4

. Write an inequality to determine the number of packages,

p

, Tatiana could buy to have enough bracelets.

Identify Known and Unknown: Identify the known quantities and the unknown variable. $\newline$ Tatiana already has $5$ bracelets and each package contains $4$ bracelets. We need to find the number of packages, $p$ , she needs to buy.
Set Up Inequality: Set up the inequality to represent the situation. $\newline$ Tatiana needs to have at least as many bracelets as there are classmates. Let's assume the number of classmates is $C$ . The total number of bracelets she will have after buying $p$ packages is $5 + 4p$ . This total must be greater than or equal to the number of classmates. $\newline$ So, the inequality is $5 + 4p \geq C$ .
Solve for p: Solve the inequality for $p$ . To find the minimum number of packages Tatiana could buy, we need to isolate $p$ in the inequality. Subtract $5$ from both sides to get: $4p \geq C - 5$ Now, divide both sides by $4$ to solve for $p$ : $p \geq (C - 5) / 4$
Interpret Inequality: Interpret the inequality. $\newline$ The inequality $p \geq \frac{C - 5}{4}$ tells us that Tatiana needs to buy at least $\frac{C - 5}{4}$ packages to have enough bracelets for her classmates. Since she cannot buy a fraction of a package, if the right side of the inequality is not a whole number, she would need to round up to the next whole number of packages.

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