Subjects algebra

Cookie Donut 485C02

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1. **State the problem:** Matilda bought packs of cookies and boxes of donut holes. The total number of cookies and donuts is given by the equation $$24c + 18d = 132$$ where $c$ is the number of cookie packs and $d$ is the number of donut boxes. She bought twice as many packs of cookies as boxes of donut holes, so we have the relation $$c = 2d$$. 2. **Substitute the relation into the total equation:** Replace $c$ with $2d$ in the total equation: $$24c + 18d = 132$$ $$24(2d) + 18d = 132$$ 3. **Simplify the equation:** $$48d + 18d = 132$$ $$66d = 132$$ 4. **Solve for $d$:** Divide both sides by 66: $$\cancel{66}d = \cancel{66} \times 2$$ $$d = 2$$ 5. **Find $c$ using $c = 2d$:** $$c = 2 \times 2 = 4$$ 6. **Answer:** Matilda bought 4 packs of cookies and 2 boxes of donut holes.