Question

Luis plans to purchase some new baseball bats and gloves before spring training begins. Luis wants to buy the same bats and gloves he purchased last spring, but he 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 current prices of these items are the same as last spring, how much will Luis pay this spring for three gloves and four bats?

Answer 1

Luis will pay for three gloves and four bats = $ 270

Explanation:

Let the bats be represented by b and gloves by g, then according to the given conditions

3b+ g= $135----equation 1

b+ 2g= $135------equation 2

Subtracting equation 2 from eq. 1 gives

3b+ g= $135----equation 1

-b -2g= -$135------equation 2

2b -g = 0 --------- equation3

2b-g= 0

or 2b= g------ equation4

This means price of 2 bats is equal to price of 1 glove.

Putting value of g in eq. 1 from eq. 4

3b+ 2b= $ 135

5b= $135

b= 135/5= 27

Price of 1 bat = $ 27 and price of 1 glove= 2*27= $54

Luis will pay for three gloves and four bats

= 54*3 + 4*27

= 162+ 108

= $ 270