MHB No problem! Glad I could help.

[Johnx1]

3 badminton racquets and 2 baseball bats cost \$167. 1 badminton racquet and 3 baseball bats cost \$163. How much does 1 badminton racquet cost?

My answer:

=> 1 badminton = 163 - 3baseball

=> 3(163 - 3 baseball) + 2 baseball = 167
= 489 - 9 baseball + 2 baseball = 167

=> 7 baseball = -322
= baseball = 46

=> 3 badminton + 2(46) = 167

so, the answer is badminton = 25Is there a better way to do this, or did I made it more difficult for me?

 

[MarkFL]

I would let \(R\) be the cost of each racquet and \(B\) be the cost of each bat. Using the information provided, I would write:

$$3R+2B=167$$

$$R+3B=163$$

I would then multiply the first equation by 3 and the second equation by -2:

$$9R+6B=501$$

$$-2R-6B=-326$$

Now, we can add the two equations, and eliminate \(B\), because we are interested in finding \(R\)

$$7R=175$$

And so:

$$R=25\quad\checkmark$$

I don't see anything wrong with what you did, except I would use single letters to represent quantities in your equations. But your method led to the correct answer.

 

[Johnx1]

I would let \(R\) be the cost of each racquet and \(B\) be the cost of each bat. Using the information provided, I would write:

$$3R+2B=167$$

$$R+3B=163$$

I would then multiply the first equation by 3 and the second equation by -2:

$$9R+6B=501$$

$$-2R-6B=-326$$

Now, we can add the two equations, and eliminate \(B\), because we are interested in finding \(R\)

$$7R=175$$

And so:

$$R=25\quad\checkmark$$

I don't see anything wrong with what you did, except I would use single letters to represent quantities in your equations. But your method led to the correct answer.

Thank you for showing me a way doing it by elimination :-)