Question

Ben bought 8 fairy sodas and 5 fairy hotdogs and spent $30.75 fairy dollars. Holly bought 7 fairy sodas and 6 fairy hotdogs and spent $33 fairy dollars? (This is systems)

Answer 1

Set up the system of equations:

$8x + 5y = 30.75$
$7x + 6y = 33$

We'll use elimination to solve this system of equations.

Take the coefficients for y in both problems. Multiply one of them by -1:

$5 \times -1 = -5$

Since this coefficient is taken from the first problem, we'll multiply the entire second problem by this negative coefficient:

$(7x + 6y = 33) \times -5 = -35x - 30y = -165$

Take the coefficient for y in the second problem and multiply the entire first problem by that coefficient:

$(8x + 5y = 30.75) \times 6 = 48x + 30y = 184.50$

Your system should now look like this:

$48x + 30y = 184.50$
$-35x - 30y = -165$

Combine these two equations to cancel out y:

$13x = 19.50$

Divide both sides by 5 to get x by itself:

$x = 1.5$

A fairy soda costs $1.50.

Because we know the value of one of the variables, we can plug it into one of the equations:

$8(1.5) + 5y = 30.75$
$12 + 5y = 30.75$

Subtract 12 from both sides:

$5y = 18.75$

Divide both sides by 5 to get y by itself:

$y = 3.75$

A fairy hotdog costs $3.75.

Answer 2

Answer:

Fairy hotdog cost 3.75, while a fairy soda costs $1.50.