Question

problems 7–9
desmos pizza’s online menu offers small, medium, and large pizzas. fill in each blank to make each equation true.
menu
small: $12 plus $1 per topping
medium: $15 plus $2 per topping
large: $18 plus $3 per topping

s(7) = m(□)
m(□) = l(5)
l(□) = s(□)

Explanation:

Step1: Define the functions

Let \( s(x) \) be the cost of a small pizza with \( x \) toppings, \( m(x) \) for medium, and \( l(x) \) for large.

• \( s(x)=12 + 1x \)
• \( m(x)=15 + 2x \)
• \( l(x)=18 + 3x \)

Step2: Solve \( s(7)=m(\square) \)

Calculate \( s(7) \):
\( s(7)=12 + 7(1)=19 \)
Set \( m(x)=19 \):
\( 15 + 2x = 19 \)
\( 2x = 4 \)
\( x = 2 \)

Step3: Solve \( m(\square)=l(5) \)

Calculate \( l(5) \):
\( l(5)=18 + 5(3)=33 \)
Set \( m(x)=33 \):
\( 15 + 2x = 33 \)
\( 2x = 18 \)
\( x = 9 \)

Step4: Solve \( l(\square)=s(\square) \)

Set \( l(x)=s(y) \):
\( 18 + 3x = 12 + y \)
Find \( x,y \) (e.g., \( x = 0 \), \( y = 6 \)):
\( l(0)=18+0=18 \), \( s(6)=12 + 6=18 \)

Answer:

• \( s(7)=m(\boldsymbol{2}) \)
• \( m(\boldsymbol{9})=l(5) \)
• \( l(\boldsymbol{0})=s(\boldsymbol{6}) \) (Note: Other solutions exist, e.g., \( x = 1, y = 9 \), but \( x = 0, y = 6 \) is a simple one.)