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Edmund bought 3 soccer balls and 6 baseball caps for $192. If 1 soccer ball costs the same as 6 baseball caps, what is the cost of 1 soccer ball and 1 baseball cap?The cost of 1 soccer ball and 1 baseball cap is $.

Question

Edmund bought 3 soccer balls and 6 baseball caps for 192.If1soccerballcoststhesameas6baseballcaps,whatisthecostof1soccerballand1baseballcap?Thecostof1soccerballand1baseballcapis192. If 1 soccer ball costs the same as 6 baseball caps, what is the cost of 1 soccer ball and 1 baseball cap?The cost of 1 soccer ball and 1 baseball cap is .

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Solution

Sure, let's solve this step by step:

  1. Let's denote the cost of a soccer ball as S and the cost of a baseball cap as C.

  2. From the problem, we know that Edmund bought 3 soccer balls and 6 baseball caps for 192.So,wecanwritethisasanequation:3S+6C=192. So, we can write this as an equation: 3S + 6C = 192.

  3. We also know that 1 soccer ball costs the same as 6 baseball caps. So, we can write this as another equation: S = 6C.

  4. Now we can substitute the second equation into the first one to solve for C. Replacing S in the first equation with 6C gives us: 3(6C) + 6C = 192.Simplifyingthisgivesus18C+6C=192. Simplifying this gives us 18C + 6C = 192, which further simplifies to 24C = $192.

  5. Solving for C, we find that C = 192/24=192 / 24 = 8. So, each baseball cap costs $8.

  6. Substituting C = 8intothesecondequationS=6CgivesusS=68 into the second equation S = 6C gives us S = 6 * 8 = 48.So,eachsoccerballcosts48. So, each soccer ball costs 48.

Therefore, the cost of 1 soccer ball and 1 baseball cap is 48+48 + 8 = $56.

This problem has been solved

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