Question

Does anyone know how to solve this problem? I am stuck. It is using solving systems of equations

Answer 1

so let's check the prices at both places.

Palanzio's

6.80 + 0.90(1)........... 1 topping

6.80 + 0.90(2)........... 2 toppings

6.80 + 0.90(3)........... 3 toppings

6.80 + 0.90(x)........... x toppings

Guido's

7.30 + 0.65(1)............1 topping

7.30 + 0.65(2)............2 toppings

7.30 + 0.65(3)............3 toppings

7.30 + 0.65(x)............x toppings

so, that is the cost equation for each one, now, if the costs were to be the same, then 6.80 + 0.90x = 7.30 + 0.65x, what's x?

$\bf \begin{cases} Palanzio's\\ 6.80+0.90x\\[-0.5em] \hrulefill\\ Guido's\\ 7.30+0.65x \end{cases}~\hspace{7em}6.80+0.90x=7.30+0.65x \\\\\\ 0.90x-0.65x=7.30-6.80\implies 0.25x=0.5\implies x=\cfrac{0.5}{0.25}\implies \boxed{x=2}$