Caps Cost 044E06

Let's solve this step by step! 🎉 **Step 1:** Understand the problem. Imagine you have caps and T-shirts. The number of caps to T-shirts is 3 : 2. **Step 2:** Let the cost of a cap be $x$ dollars. Then, the cost of a T-shirt is $x + 5.50$ dollars. **Step 3:** Number of caps = 3 parts, number of T-shirts = 2 parts. **Step 4:** Total cost of caps = number of caps × cost per cap = $3x$ **Step 5:** Total cost of T-shirts = number of T-shirts × cost per T-shirt = $2(x + 5.50) = 2x + 11$ **Step 6:** Mr. Yong spent $259 more on caps than T-shirts: $$3x = (2x + 11) + 259$$ **Step 7:** Solve the equation: $$3x = 2x + 11 + 259$$ $$3x = 2x + 270$$ $$3x - 2x = 270$$ $$x = 270$$ **Step 8:** The cost of each cap is $270 dollars! 🎯 **Step 9:** Check total payment: Cost of caps: $3 imes 270 = 810$ Cost of T-shirts: $2 imes (270 + 5.50) = 2 imes 275.50 = 551$ Sum: $810 + 551 = 1361$ which is less than $2219$, so we must check again. **Step 10:** Use total money spent $2219$: Total cost = caps + T-shirts $$3x + 2(x + 5.50) = 2219$$ $$3x + 2x + 11 = 2219$$ $$5x + 11 = 2219$$ $$5x = 2208$$ $$x = 441.6$$ **Step 11:** So, the cost of each cap is $441.60$ dollars. **Final answer:** Cost of each cap = $441.60$ ➕ = Great job! 🎉 You found the cost of each cap!