To make the solution easier to follow, let's replace the word
bat with
helmet.
sud21 wrote:A sporting good store sells one type of baseball helmet and one type of baseball. The cost for 2 helmets and 4 balls is $160. The cost for 1 helmet and 6 balls is $160, as well. If someone were to buy an equal number of helmets and balls, at most how many helmets can he purchase if he has a budget of $240 for the purchase?
2
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6
Let h - the cost of a helmet and b = the cost of a ball.
The cost for 2 helmets and 4 balls is $160:
2h + 4b = 160.
The cost for 1 helmet and 6 balls is $160
h + 6b = 160.
Since replacing 1 helmet with 2 balls does not change the total cost, the cost of 1 helmet must be equal to the cost of 2 balls:
h = 2b.
Substituting h = 2b into h + 6b = 160, we get:
2b + 6b= 160
8b = 160
b = 20.
Since b=20 and h=2b, h=40.
Since b=20 and h=40, we get:
b+h = 60.
4b + 4h = 240.
Thus, a budget of $240 allows for the purchase of 4 bats and 4 helmets.
The correct answer is
C.
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