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 $=\mathrm{\$}17}$

Selling price of scientific calculator $=\mathrm{\$}12}$

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 $=40+20\times minutes$

$Minutes=\frac{Points-40}{20}\Rightarrow \left\{equation\left(1\right)\right\}$

For Mona;

Points $=20+25\times minutes$

$Minutes=\frac{Points-20}{25}\Rightarrow \left\{equation\left(2\right)\right\}$

To find the number of minutes until Mona overtakes Ahmed.

Let Mona overtakes Ahmed in 'x' minutes, then from equation (1) and equation (2)

$x=\frac{P\oint s-40}{20}$

Also, $x=\frac{P\oint s-20}{25}$

$\frac{P\oint s-40}{20}=\frac{P\oint s-20}{25}$

$25\text{}Points-1000=20\text{}Points-400$

$25\text{}Points-20\text{}Points=1000-400$

$5\text{}Points=600$

Points $=120$

Putting these points in equation (1) or equation(2), then we get the minutes until Mona overtakes Ahmed.

$Minutes=\frac{Points-20}{25}$

$=\frac{120-20}{25}$

$Minutes=4$

Step 3

b) Let the number of graphic calculator were sold $=X$

And the number of scientific calculator were sold $=Y$

It is given that the total number of calculators were sold $=100$,

It means,

$X+Y=100\Rightarrow$ equation(1)

$17X+12Y=1550\Rightarrow$ equation(2)

multiplying by 12 in equation(1) and the result subtract from equation(2)

$(17X+12Y)-(12X+12Y)=1550-12\times 100$

$5X=350$

$X=70$ (Number of graphic calculator)

Putting the value of X in equation (1)

$70+Y=100$

$Y=30$ (number of Scientific calculator)

Step 4

Answer:

a) The equation that can be used to find minutes is

For Ahmed

$Minutes=\frac{Points-40}{20}$

For Mona;

$Minutes=\frac{Points-20}{25}$

The number of minutes until Mona overtakes Ahmed $=4$ minutes

b) The number of graphic calculators were sold $=70$

The number of scientific calculators were sold $=30$