A sporting good store sells one type of baseball bat and one type of b

Question

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

Kudos for a correct solution.

A. 2
B. 3
C. 4
D. 5
E. 6

Kudos for a correct  solution .

Celestial09 · Answer

Hi,
IMO it should be C that is 4
reason:
formed an equation... bat = b ball = c
2b+4c=160
1b+6c=160

solving both we get b that is bat = 40 and c that is ball = 20
new equation 240 to be divided in equal
4b+4c=240
4*40 + 4*20 = 240
160 + 80 = 240

Kudos , if its a correct solution. 
kindly share a simpler method possible.

Lucky2783 · Answer

from " The cost for 2 bats and 4 balls is $160. The cost for 1 bat and 6 balls is $160 " we know that  Cost_{Bat} = 2*Cost_{Ball} 
so,  Cost_{Bat} = 40  and  Cost_{Ball}=20

hence , If someone were to buy an equal number of bats and balls , he could buy 4 Bats and 4 Balls. (40X+20X=240)

Answer C.

shriramvelamuri · Answer

Two equation problem. .

2x+4y=160
x+6y=160.

Solving we get X and Y. X+Y= 60. Because he buy equal number of bats and balls; he could buy 4 sets and the answer is C.

EMPOWERgmatRichC · Answer

Hi All,

While most Test Takers would probably do "System" Algebra to solve this question (which is a perfectly acceptable approach to this question), there's also a pattern-matching shortcut built into it that provides another option.

We're told that two sets of items that can be purchased for $160
2 bats + 4 balls = $160
1 bat + 6 balls = $160

Looking at this data, we can see that "trading" 1 bat will get you 2 balls at the same price. Thus, the price of 1 bat = the price of 2 balls.

We're asked to buy the SAME number of bats and balls with $240....

$240 = (1.5)($160)

Using that first equation, we can multiply all of the terms by 1.5, which gives us...

2(1.5) bats + 4(1.5) balls = $160(1.5)

3 bats + 6 balls = $240

Noting the earlier "trade" option, we can "trade" 2 balls for 1 bat....this gives us....

4 bats + 4 balls = $240

So the MOST bats that can be purchased under these conditions is 4.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

KS15 · Answer

Cost of 1 bat=x and cost of one ball=y (say)
2x+4y=160
x+6y=160

Solving both equations,
8y=160
y=20
x=40
Now, Total Budget=$240
If x=40 and y=20
we can get only one combination which satisfies the given conditions.
We can buy 4 bats and 4 balls
i.e ($40*4)+($20*4)=$240
Answer C

SherLocked2018 · Answer

BB = bat , B = ball, we are given : 
2BB + 4B = 160
BB + 6B = 160
Thus solving : BB = 40, and B = 20. Now if same no of BB and B total 240 => no of B = 4. 
Ans C.

Bunuel · Answer

VERITAS OFFICIAL SOLUTION:

This word problem starts you off with two equations. If you assign variables as x = bats and y = balls, you have:

2x + 4y = 160, which reduces to x + 2y = 80

and

x + 6y = 160

You can then use the Elimination Method to eliminate the x terms and solve for y:

x + 6y = 160

-x - 2y = -80

4y = 80, so y = 20. Plug that back in, and x = 40. So now you have the prices.

At this point, you know that you need the same number of x and y, and that the total can only be as high as 240. If you call that same number a, you have:

20a + 40a = 240

60a = 240

a = 4. So you'll be able to buy 4 bats and 4 balls, making the answer C.

pacifist85 · Answer

Hello,

I also used the same method (solving the two equations) to find the price for each bat and each ball. But then, since we need then to be equal, i just added one bat and one ball each time until i reached 240.

x...........y...........cost
40........20...........60 --> here we could do 60x=240 --> x = 4 and get it done with. But I didn't....
40........20...........120
40........20...........180
40........20...........240. So, we would buy 4 of each.

law258 · Answer

2B+4A=160
1B+6A=160

(A=balls & B = bats)

Solve this system of equations --> You'll find A = $20 & B = $40

C is the only option that will give you $240 exactly.

ScottTargetTestPrep · Answer

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

Archit3110 · Answer

let cost of each bat be x and that of ball be y
2x+4y= 160 and
x+6y=160
solve for x &y ; x= $40 and y ; $20
given that 
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
or say ; 40a+20a= 240
60a= 240
a= 40
OPTION C

5thEagle · Answer

Solve the system of equations to get 1 ball = 2 bats in cost, then you can approach this in a bunch of different ways. Too used to my algebra days, I plugged back in to find a ball is $40 and a bat is $20, then solved the system of equations to get both of the amounts simultaneously.

I think the easiest way to do this is using the shortcut noted above by Empower though.

I think the easiest way to do this is using the shortcut noted above by Empower though.

A sporting good store sells one type of baseball bat and one type of b

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A sporting good store sells one type of baseball bat and one type of b

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