Question

read the instructions first and graph​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

Let number of Cheese pizza be 'x'

and

Let number of Peperoni pizza be 'y'.

☆ According to first condition, you need to sell atleast 20 pizza's of both types.

$: \implies \: \tt \: x \: + \: y \: \geqslant \: 20 \: - - - (1)$

☆ According to second condition, cost of cheese pizza is 8 pesos and cost of Peperoni pizza is 9 pesos and you need to sell pizza's of atleast 180 pesos.

$: \implies \: \tt \: 8x \: + \: 9y \: \geqslant \: 180$

Graph :-

$\begin{gathered}\bf\blue{x\:+\:y\:=\:20} \\ \end{gathered}$

❶ Substituting 'x = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{0\:+\:y\:=\:20} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{y\:=\:20} \\ \end{gathered}$

❷ Substituting 'y = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{x\:+\:0\:=\:20} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:20} \\ \end{gathered}$

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 20 \\ \\ \sf 20 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 20) & (20 , 0)

Graph :-

$\begin{gathered}\bf\blue{8 \: x\:+9\:y\:=\:180} \\ \end{gathered}$

❶ Substituting 'x = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{8\times{0}\:+9\:y\:=\:180} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{0\:+9\:y\:=\:180} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{y\:=\:20} \\ \end{gathered}$

❷ Substituting 'y = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{9\times{0}\:+8\:x\:=\:180} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{0\:+\:8x\:=\:180} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:22.5} \\ \end{gathered}$

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 20 \\ \\ \sf 22.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 20) & (22.5 , 0)

Answer 2

Step-by-step explanation:

Polya's method:-

a) Understanding the problem:-

Let X be the number of cheese Pizza

and Y be the number of pepperoni Pizza

b) Devise a plan:-

X+Y≥20 ------(1)

8X+9Y≥180 ----(2)

C) Carryout a plan:-

Y≥ -X+20

Y≥ -8/9 X+20

D)Look back:-

(12,10)

12+10≥20

22≥20

and

8(12)+9(10)≥180

=>96+90≥180

>186≥180

Steps in Polya's method:-

• Understanding the problem
• Devise a plan
• Carryout a plan
• Look back