Question

At Big Al’s hot dog stand, two hot dogs and three sodas cost $7. The costof four hot dogs and two sodas is $10. Determine the cost of a hot dogand the cost of a soda. How can I set up a system of equations to represent the scenario above? This is how far I got but I'm not sure I'm on the right path. Hotdog = XSoda = Yx2 + y3 = 7x4 + y2 = 10

Answer 1

ANSWER

$x=2,\text{ y=1}$

EXPLANATION

Let the hot dog be represented by x,

Let (y) represent soda

For "two hot dogs and three soda costs $7" this means;

$2x+3y=7\ldots\ldots\ldots\ldots1$

For "the cost of four hot dogs and two sodas is $10" we have;

$4x+2y=10\ldots\ldots\ldots..2$

Now, using elimination method, we multiply equation 1 by 2 and equation 2 by 1 so as to eliminate x

Hence, we have;

$\begin{gathered} 2x+3y=7\ldots\ldots\ldots\ldots1\times2 \\ 4x+6y=14\ldots\ldots\ldots.3 \end{gathered}$

Now to eliminate x, we subtract equation 2 from 3

so, we have;

$\begin{gathered} 4x-4x+6y-2y=14-10 \\ 4y=4 \\ y=1 \end{gathered}$

Now substitute the value of y into equation 1 to get x

$\begin{gathered} 2x+3y=7 \\ 2x+3(1)=7 \\ 2x+3=7 \\ 2x=7-3 \\ 2x=4 \\ x=\frac{4}{2} \\ x=2 \end{gathered}$

Therefore the cost of 1 hot dog is $2 while that of soda is $1