At a concession stand, seven hot dog (s )and two hamburger (s )cost $16.75; two hot dog (s )and seven hamburger (s )cost $19.25.

Question

3 years ago

7

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

1 answer:

Eddi Din [679] · Answer 1 · 2022-04-03T00:50:00+03:00

One hot dog costs $1.75 and one hamburger costs $2.25

Step-by-step explanation:

Let,

Hot dog = x

Hamburger = y

According to given statement;

7x+2y=16.75 Eqn 1

2x+7y=19.25 Eqn 2

Multiplying Eqn 1 by 2;

$2(7x+2y=16.75)\\14x+4y=33.50\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 7;

$7(2x+7y=19.25)\\14x+49y=134.75\ \ \ Eqn\ 4$

Subtracting Eqn 3 from Eqn 4;

$(14x+49y)-(14x+4y)=134.75-33.50\\14x+49y-14x-4y=101.25\\45y=101.25$

Dividing both sides by 45;

$\frac{45y}{45}=\frac{101.25}{45}\\y=2.25$

Putting y=2.25 in Eqn 1

$7x+2(2.25)=16.75\\7x+4.50=16.75\\7x=16.75-4.50\\7x=12.25$

Dividing both sides by 7;

$\frac{7x}{7}=\frac{12.25}{7}\\x=1.75$

One hot dog costs $1.75 and one hamburger costs $2.25

Keywords: linear equations, subtraction

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