Easy (but kinda tricky) math problem help?

Question

My teacher posted this just for fun math question, so I looked at it and although its not for extra credit or anything, I want to know how to solve this. I'm just curious! Here is the problem:

"Luis plans to purchase some new baseball bats and gloves before spring training begins. He wants to get the same bats and gloves he purchased last spring, but can’t remember the price of each item. Luis recalls making two purchases last spring, each totaling $135 and both tax exempt. The first purchase was for a glove and three bats. The second purchase was for two gloves and a bat. If the prices of these items are the same as last spring, how much will Luis pay for three gloves and four bats?"

Can you please show me your steps and explain to me how you got to your answer? Thank You! :)

Anonymous · Accepted Answer

This is a system of equations problem: We have 2 equations with x (bats) and y (gloves).
The purchases become the following 2 equations:
x+3y=135
2x+y=135. 
We can use substitution or elimination to solve. 
Substitution will tell us to solve for a variable, and then use our solution in the other equation to solve for our value. In equation one, we can subtract 3 y from each side to solve for x
x= 135-3y. 

We then substitute that into the second equation. 2(135-3y) +y = 135.
270 -6y +y =135. Subtract 270 from each side and simplify
-5y= -135 and y= -135/-5 = $27 for each bat.
Plug that into our x= 135-2y to get 135 - 3(27)= 135-81= $54 per bat.

plug it in to try it out:
54+ 3(27)= 54+81= 135
2(54)+ 27= 108+27= 135.

? · Answer

First, a million.5 miles = 7920 ft. next, 7920 divided by ability of 15 = 528 So there are 528 15-foot distances on the two aspects of the line. yet you ought to contain the barrel on the commencing up of each row: so there are easily 529 barrels on the two aspects, for an entire of 1058 barrels.

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Easy (but kinda tricky) math problem help?

2 Answers