1) Ahmed and Mona are competing on a quiz app. Ahmed has 40 points already...

Step 1
Ahmed has 40 points already and is wining 20 points per minute.
Mona has 20 points already and is wining 25 points per minute.
after m minutes Mona overtakes Ahmed
Step 2
1) according to question
Ahmed points after m minutes ${\displaystyle =40+20m}$
Mona points after m minutes ${\displaystyle =20+25m}$
${\displaystyle 40+20m=20+25m}$
${\displaystyle 25m-20m=40-20}$
${\displaystyle 5m=20}$
${\displaystyle m=4}$ minutes so after 4 minutes Mona ahead Ahmed
2) graphing calculator price ${\displaystyle =\mathrm{\$}17}$
scientific calculator price ${\displaystyle =\mathrm{\$}12}$
let graphic calculators sold ${\displaystyle =x}$
scientific calculators sold ${\displaystyle =y}$
total sold ${\displaystyle =100}$
${\displaystyle x+y=100}$ (1)
total money earned ${\displaystyle =\mathrm{\$}1550}$
${\displaystyle 17x+12y=17550}$ (2)
equation (2) -equation(1)*12
${\displaystyle (17x+12y)-(12x+12y)=1550-12\cdot 100}$
${\displaystyle 5x=1550-1200}$
${\displaystyle 5x=350}$
${\displaystyle x=70}$
${\displaystyle y=100-70=30}$
graphic calculators sold ${\displaystyle =70}$
scientific calculators sold ${\displaystyle =30}$

Step 1
Given:
a) Ahmad has 40 points already and winning 20 points per minute
Mona has 30 points already and winning 25 points per minute
b) Selling price of graphing calculator ${\displaystyle =\mathrm{\$}17}$
Selling price of scientific calculator ${\displaystyle =\mathrm{\$}12}$
On the first day of classes 100 calculators were sold for a total of $1,550
Step 2
Solution:
a) The equation that can be used to find m, the number of minutes
For Ahmed;
Points ${\displaystyle =40+20\times minutes}$
${\displaystyle Minutes=\frac{Points-40}{20}\Rightarrow \left\{equation\left(1\right)\right\}}$
For Mona;
Points ${\displaystyle =20+25\times minutes}$
${\displaystyle Minutes=\frac{Points-20}{25}\Rightarrow \left\{equation\left(2\right)\right\}}$
To find the number of minutes until Mona overtakes Ahmed.
Let Mona overtakes Ahmed in 'x' minutes, then from equation (1) and equation (2)
${\displaystyle x=\frac{P\oint s-40}{20}}$
Also, ${\displaystyle x=\frac{P\oint s-20}{25}}$
${\displaystyle \frac{P\oint s-40}{20}=\frac{P\oint s-20}{25}}$
${\displaystyle 25Points-1000=20Points-400}$
${\displaystyle 25Points-20Points=1000-400}$
${\displaystyle 5Points=600}$
Points ${\displaystyle =120}$
Putting these points in equation (1) or equation(2), then we get the minutes until Mona overtakes Ahmed.
${\displaystyle Minutes=\frac{Points-20}{25}}$
${\displaystyle =\frac{120-20}{25}}$
${\displaystyle Minutes=4}$
Step 3
b) Let the number of graphic calculator were sold ${\displaystyle =X}$
And the number of scientific calculator were sold ${\displaystyle =Y}$
It is given that the total number of calculators were sold ${\displaystyle =100}$,
It means,
${\displaystyle X+Y=100\Rightarrow }$ equation(1)
${\displaystyle 17X+12Y=1550\Rightarrow }$ equation(2)
multiplying by 12 in equation(1) and the result subtract from equation(2)
${\displaystyle (17X+12Y)-(12X+12Y)=1550-12\times 100}$
${\displaystyle 5X=350}$
${\displaystyle X=70}$ (Number of graphic calculator)
Putting the value of X in equation (1)
${\displaystyle 70+Y=100}$
${\displaystyle Y=30}$ (number of Scientific calculator)
Step 4
Answer:
a) The equation that can be used to find minutes is
For Ahmed
${\displaystyle Minutes=\frac{Points-40}{20}}$
For Mona;
${\displaystyle Minutes=\frac{Points-20}{25}}$
The number of minutes until Mona overtakes Ahmed ${\displaystyle =4}$ minutes
b) The number of graphic calculators were sold ${\displaystyle =70}$
The number of scientific calculators were sold ${\displaystyle =30}$

According to question Ahmed points after m minutes =40+20m Mona points after m minutes = 20 +25m 40 + 20m = 20+ 25m 25m - 20m = 40 -20 5m = 20 m = 4 minutes so after 4 minutes Mona ahead Ahmed Graphing calculator price = $17 scientific calculator price = $12 let graphic calculators sold = x scientific calculators sold = y total sold =100 x+y=100 (1) total money earned =$1550 17x +12y = 17550 (2) equation (2) -equation(1)*12 (17x +12y) -(12x +12y) = 1550 - 12 * 100 5x = 1550 -1200 5x = 350 x = 70 y = 100-70 = 30 graphic calculators sold =70 scientific calculators sold =30