A sporting good store sells one type of baseball bat and one type of baseball. The cost for \(2\) bats and \(4\) balls

[Vincen]

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

Source: Veritas Prep

[Scott@TargetTestPrep]

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

Solution:

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