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A cupcake requires $35$ grams of sugar and $50$ grams of flour, and a muffin requires $30$ grams of sugar and $65$ grams of flour. Shawna needs to use up at least $460$ grams of sugar to make cupcakes and muffins, and she wants to use at most $970$ grams of flour. Let $C$ denote the number of cupcakes she makes and $M$ the number of muffins she makes. Write an inequality that represents the condition based on the number of grams of sugar.

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One-step inequalities: word problems

Full solution

Q. A cupcake requires

35

grams of sugar and

50

grams of flour, and a muffin requires

30

grams of sugar and

65

grams of flour. Shawna needs to use up at least

460

grams of sugar to make cupcakes and muffins, and she wants to use at most

970

grams of flour. Let

C

denote the number of cupcakes she makes and

M

the number of muffins she makes. Write an inequality that represents the condition based on the number of grams of sugar.

Identify Sugar Inequality: We need to find the inequality for sugar. Each cupcake uses $35$ grams of sugar and each muffin uses $30$ grams of sugar.
Define Variables: Let $C$ be the number of cupcakes and $M$ be the number of muffins. The total sugar used is $35C + 30M$ .
Formulate Inequality: Shawna needs to use at least $460$ grams of sugar. So, the inequality is $35C + 30M \geq 460$ .

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