Subjects algebra

Gift Shares B586E6

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1. **State the problem:** Macy, Daisy, and Leo share the cost of a gift. Macy's share is $320 less than 6 times Daisy's share. Leo's share is $184 more than 4 times Daisy's share. Macy's and Leo's shares are equal. We need to find Daisy's share and determine if the gift costs more than 2500. 2. **Define variables:** Let Daisy's share be $d$. 3. **Write expressions for Macy's and Leo's shares:** - Macy's share = $6d - 320$ - Leo's share = $4d + 184$ 4. **Set Macy's share equal to Leo's share:** $$6d - 320 = 4d + 184$$ 5. **Solve for $d$:** $$6d - 320 = 4d + 184$$ $$6d - \cancel{320} - 4d = 4d + 184 - \cancel{320} - 4d$$ $$2d - 320 = 184$$ $$2d = 184 + 320$$ $$2d = 504$$ $$d = \frac{504}{2}$$ $$d = 252$$ 6. **Find Macy's and Leo's shares:** - Macy's share = $6(252) - 320 = 1512 - 320 = 1192$ - Leo's share = $4(252) + 184 = 1008 + 184 = 1192$ 7. **Find total cost of the gift:** $$\text{Total} = d + \text{Macy's share} + \text{Leo's share} = 252 + 1192 + 1192 = 2636$$ 8. **Answer part (b):** Since $2636 > 2500$, the gift costs more than 2500. **Final answers:** (a) Daisy's share is $252$. (b) Yes, the gift costs more than 2500 because the total is $2636$.