Question 1103318: Three baseball bats and five baseball gloves cost $235. Two bats and six gloves cost $210. Find the cost of a baseball glove. Found 2 solutions by algebrahouse.com, greenestamps:Answer by algebrahouse.com(1659) (Show Source):
-6b - 10g = -470 {multiplied top equation by -2}
6b + 18g = 630 {multiplied bottom equation by 3}
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8g = 160 {added the two equations}
g = 20 {divided each side by 8}
The solution by algebrahouse is a perfectly good formal solution.
If you can and want to be a bit less formal, you might do something like this....
(1) 3 bats and 5 gloves cost $235
(2) 2 bats and 6 gloves cost $210
From (2), we can conclude that
(3) 1 bat and 3 gloves cost $105
(Note I divided equation (2) by 2 to get equation (3). The other tutor's solution would have been shorter and easier if he had done the same....)
Now from (2) and (3) we can conclude that
(4) 3 bats and 9 gloves cost $315
Now comparing the purchases in equations (1) and (4), we see that 4 gloves cost $80. (The numbers of bats are the same in the two equations, so the difference in cost is because of the different numbers of gloves.)
