Question

Robert took $50 with him to spend on pizza and games for himself and his friends at Chucky Cheese. The price for each slice of pizza was $5. The price of each game was half the price of a slice of pizza.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of slices of pizza and the other axis to represent the number of games.
(b) What do the intercepts and the solutions of your graphed function mean in context of the problem?

Answer 1

Answer-

Equation for this situation,

$\boxed{\boxed{y=20-2x}}$

Solution-

The total amount of money that Robert has = $50

Price of each slice of pizza = $5

Price of each game = $$\dfrac{5}{2}$= $2.5

Let x = number of pizza he can buy, and y = number of game he can play

So,

$\Rightarrow (5\times x)+(2.5\times y)=50$

$\Rightarrow 5x+2.5y=50$

$\Rightarrow 2.5y=50-5x$

$\Rightarrow y=\dfrac{50-5x}{2.5}=\dfrac{50}{2.5}-\dfrac{5x}{2.5}$

$\Rightarrow y=20-2x$

Plotting the graph we get the intercepts as,

x- intercepts = 10

y- intercepts = 20

x- intercepts is the point where, y=0, so in this case if does not play any game he can buy 10 slices of pizza.

y- intercepts is the point where, x=0, so in this case if he does not eat any pizza he can play 20 games.