Caleb spends $72.50 on 50 hamburgers for the marching band. If single

Question

Caleb spends $72.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?

A. 5
B. 10
C. 20
D. 40
E. 45

Kudos for a correct  solution .

balamoon · Answer

Caleb spends $72.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?

A. 5
B. 10
C. 20
D. 40
E. 45

Solution -

Lets say, Single hamburgers  x  and Double hamburgers  y 
Given that, 
 x+y=50 and 1x+1.5y=72.50. By solving the equations y=45. ANS E.

Thanks
Kudos Please

GMATinsight · Answer

No. of Single Burger = S
No. of Double Burger = D

$1*S + $1.5*D = 72.50-----------Equation (1)

Total Burgers = S + D = 50-----------Equation (2)

Solving the two equations Simultaneously

($1*S + $1.5*D) - (S + D) = 72.5 - 50

0.5*D = 22.5

i.e. D = 45
i.e. S = 50-45 = 5

Answer: Option E

adityadon · Answer

suppose no. of single burger is x , and no. of double burger is y

So , x+ y = 50 ------1 
and x +1.5 y = 72.5 ------2

Substract eqn 1 from 2

we get , 0.5 y= 22.5 
so y =45

answer is E

TimeTraveller · Answer

x+1.5y = 72.5
x+y = 50
------------------
0.5y = 22.5
y = 45, Ans is E.

lipsi18 · Answer

Let # of single burger=x , # of double =y
So we have x+y=50 ---1
We also have x*1+y*1.5 =72.5 =>2x+3y=145 ----2
With equation 1 &2 we can find out y =45

Hence answer is E
Thanks,

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Let s = the number of single burgers purchased
Let d = the number of double burgers purchased

Caleb bought 50 burgers: s + d = 50

Caleb spent $72.50 in all: s + 1.5d = 72.50

Combine the two equations by subtracting equation 1 from equation 2.

s + 1.5d = 72.50
-(s + d = 50)
______________
0.5d = 22.5

d = 45.

Answer: E.

Mo2men · Answer

single burger= x
double burger =y

(1)x+ (1.5)y= 72.5

Although there is another equation x+y=50. I ignore it. I looked into the answer choice which I can multiply in 1.5 and its tenth digit 0.5 so when subtracting from 72.5 give me integer number. Two choices give 5 & 45. Logically stares with 45

x +(1.5) 45= 72.5..........x= 72.5- 67.5 = x=5 so 5+45=50

answer E

jennisa · Answer

Well, I didn't solve it this way, but I believe that this method works as well.
$1x+ $1.5x= $72.5
So, $2.5x= $72.5
So, x= 29
So 1*29= 29 single burgers and 
1.5* 29= 43.5 double burgers 
It's not 45, but it's not either any of the other choices, so choice E is the closest.
What do you think Bunuel?

ashishahujasham · Answer

Bunuel can you please tell why the above method I'd wring silver by jennisa

Sent from my A1601 using  GMAT Club Forum mobile app

Bunuel · Answer

No, that method is not correct.  jennisa  assumes that the number of single and double burgers is the same, hence she denotes both of them by x (in the correct solution we denoted those with s and d). Next, when she multiplies x (the # of burgers) by $1.5, she gets the amount of money but she assumes it's the number of double burgers, which is wrong.

susheelh · Answer

Though many people have solved by using the Algebraic method, I guess this can also be solved by looking at the answer choice.

Since the Double burger cost is $1.5, single burger is $1 and total is $72.5, the number of Double burger HAS to be odd. If not, the total cost will not end with 0.5. This Eliminates B,C,D. Answer is either A or E. A quick check will confirm that E is the correct answer.

JeffTargetTestPrep · Answer

We can let x = the number of single burgers and y = the number of double burgers, and thus we can create the following two equations:

x + y = 50

and

x + 1.5y = 72.50

If we subtract the first equation from the second, we have:

0.5y = 22.50

Multiply both sides by 2, we have:

y = 45

Answer: E

Abhishek009 · Answer

s + d = 50 ------------------->(I)

Now,  1*s + \frac{3d}{2} = \frac{725}{10}

Or,  \frac{10s}{10} + \frac{15d}{10} = \frac{725}{10}

Or,  10s + 15d = 725

Or,  2s + 3d = 145 ------------------->(II)

(I) *2 = >  2s + 2d = 100 ------------------->(III)

Now, (II) - (III) =>  d = 45 , Hence Answer must be (E) 45

Caleb spends $72.50 on 50 hamburgers for the marching band. If single

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Caleb spends $72.50 on 50 hamburgers for the marching band. If single

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