Math

QuestionShawna needs to make cupcakes and muffins using at least 460g of sugar and at most 970g of flour. A cupcake requires 3535g of sugar and 5050g of flour, while a muffin requires 3030g of sugar and 6565g of flour. Write inequalities to represent the conditions based on sugar and flour.

Studdy Solution

STEP 1

Assumptions
1. A cupcake requires 35 grams of sugar.
2. A cupcake requires 50 grams of flour.
3. A muffin requires 30 grams of sugar.
4. A muffin requires 65 grams of flour.
5. Shawna needs to use at least 460 grams of sugar.
6. Shawna wants to use at most 970 grams of flour.
7. Let CC denote the number of cupcakes Shawna makes.
8. Let MM denote the number of muffins Shawna makes.

STEP 2

We will first write an inequality for the sugar condition. The total amount of sugar used must be at least 460 grams. Since each cupcake uses 35 grams of sugar and each muffin uses 30 grams of sugar, the inequality will be based on the number of cupcakes and muffins Shawna makes.
35C+30M46035C + 30M \geq 460

STEP 3

Next, we will write an inequality for the flour condition. The total amount of flour used must be at most 970 grams. Since each cupcake uses 50 grams of flour and each muffin uses 65 grams of flour, the inequality will be based on the number of cupcakes and muffins Shawna makes.
50C+65M97050C + 65M \leq 970

STEP 4

The inequalities representing the conditions based on the number of grams of sugar and flour are:
For sugar: 35C+30M46035C + 30M \geq 460
For flour: 50C+65M97050C + 65M \leq 970
These inequalities must be satisfied simultaneously to meet Shawna's requirements for making cupcakes and muffins using the given amounts of sugar and flour.

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