At a concession stand, seven hot dogs and two hamburgers cost 14.50, two hot dogs and seven hamburgers cost 17.00. Find the cost of one hot dog and the cost of one hamburger

Given:

Seven hot dogs and two hamburgers cost 14.50

Two hot dogs and seven hamburgers cost 17.00.

To find:

The cost of one hot dog and the cost of one hamburger.

Solution:

Let the cost of one hot dog be x and the cost of one hamburger be y.

According to the question,

[tex]7x+2y=14.50[/tex]       ...(i)

[tex]2x+7y=17.00[/tex]       ...(ii)

Multiply (i) by 7.

[tex]49x+14y=101.5[/tex]       ...(iii)

Multiply (ii) by 2.

[tex]4x+14y=34.00[/tex]       ...(iv)

Subtract (iv) from (iii).

[tex]49x-4x=101.5-34[/tex]  

[tex]45x=67.5[/tex]  

Divide both sides by 45.

[tex]x=1.5[/tex]  

Put x=1.5 in (i).

[tex]7(1.5)+2y=14.50[/tex]

[tex]10.50+2y=14.50[/tex]

[tex]2y=14.50-10.50[/tex]

[tex]2y=4[/tex]

Divide both sides by 2.

[tex]y=2[/tex]

Therefore, the cost of one hot dog is 1.5 and the cost of one hamburger is 2.

Answer:

the other person is correct

Step-by-step explanation:

i put in the answers and it’s correct

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