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 $2636$.
Gift Shares B586E6
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