A sporting good store sells one type of baseball bat and one type of baseball. The cost for \(2\) bats and \(4\) balls is \(\$160.\) The cost for \(1\) bat and 6 balls is \(\$160,\) as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of \(\$240\) for the purchase?
A. 2
B. 3
C. 4
D. 5
E. 6
Answer: C
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A sporting good store sells one type of baseball bat and one type of baseball. The cost for \(2\) bats and \(4\) balls
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Solution:Vincen wrote: ↑Wed Oct 28, 2020 8:35 amA sporting good store sells one type of baseball bat and one type of baseball. The cost for \(2\) bats and \(4\) balls is \(\$160.\) The cost for \(1\) bat and 6 balls is \(\$160,\) as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of \(\$240\) for the purchase?
A. 2
B. 3
C. 4
D. 5
E. 6
Answer: C
We can let b = the cost for a ball and t = the cost for a bat, thus:
2t + 4b = 160
t + 2b = 80 (1)
and
t + 6b = 160 (2)
Subtracting equation one from equation two, we have:
4b = 80
b = 20
So t = 40
We can let n = the number of bats and balls, and create the equation:
20n + 40n = 240
60n = 240
n = 4
Answer: C
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