Question

On Wednesday, a local hamburger shop sold a combined total of 261 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Wednesday?

Answer 1

Step-by-step explanation:

Let x be the no. of hamburgers and y be the no. of cheeseburgers.

According to the question,

x+y=261...............(1)

2x=y.............(2)

put (2) in (1)

x+2x=261

3x=261

x=87

Therefore, the no. of hamburgers sold on wednesday were 87

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Answer 2

Let us assume that on Wednesday, a local hamburger shop sold 'M' hamburgers and 'N' cheeseburgers.

Given that, he sold a total of 261 hamburgers and cheeseburgers.

Hamburgers + Cheeseburgers = 261

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

$\implies\:\sf{M+N\:=\:261}$

$\implies\:\sf{M\:=\:261-N}$

Also given that, the number of cheeseburgers sold was two times the number of hamburgers sold.

Cheeseburgers = 2 × Hamburgers

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

$\implies\:\sf{N\:=\:2M}$

Substitute value of N in M

$\implies\:\sf{M\:=\:261-(2M)}$

$\implies\:\sf{M\:=\:261-2M}$

$\implies\:\sf{M+2M\:=\:261}$

$\implies\:\sf{3M\:=\:261}$

$\implies\:\sf{M\:=\:\frac{261}{3}}$

$\implies\:\sf{M\:=\:87}$

Substitute value of M in N

$\implies\:\sf{N\:=\:2(87)}$

$\implies\:\sf{N\:=\:174}$

Therefore,

The number of Hamburgers that were sold on Wednesday = 87 and Cheeseburgers = 174.

$\rule{250}2$

Verification

From the above calculations, we have a number of Hamburgers = M = 87 and Cheeseburgers = N = 174

Case 1.

“He sold a total of 261 hamburgers and cheeseburgers.”

⇒ M + N = 261

⇒ 87 + 174 = 261

Case 2.

“The number of cheeseburgers sold was two times the number of hamburgers sold.”

⇒ N = 2M

⇒ 174 = 2(87)

⇒ 174 = 174