kloseyq

2021-12-18

1) Ahmed and Mona are competing on a quiz app. Ahmed has 40 points already and is wining 20 points per minute. Mona has 20 points already and is wining 25 points per minute.
Write an equation that can be used to find m, the number of minutes until Mona overtakes Ahmed.
2)The campus bookstore sells graphing calculators for $17 and scientific calculators for$12. On the first day of classes 100 calculators were sold for a total of $1,550. How many of each were sold? (Solve algebraically) ### Answer & Explanation Thomas Nickerson Beginner2021-12-19Added 32 answers 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 $=40+20m$ 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 2) graphing calculator price $=\mathrm{}17$ scientific calculator price $=\mathrm{}12$ let graphic calculators sold $=x$ scientific calculators sold $=y$ total sold $=100$ $x+y=100$ (1) total money earned $=\mathrm{}1550$ $17x+12y=17550$ (2) equation (2) -equation(1)*12 $\left(17x+12y\right)-\left(12x+12y\right)=1550-12\cdot 100$ $5x=1550-1200$ $5x=350$ $x=70$ $y=100-70=30$ graphic calculators sold $=70$ scientific calculators sold $=30$ lenkiklisg7 Beginner2021-12-20Added 29 answers 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 $=40+20×minutes$
$Minutes=\frac{Points-40}{20}⇒\left\{equation\left(1\right)\right\}$
For Mona;
Points $=20+25×minutes$
$Minutes=\frac{Points-20}{25}⇒\left\{equation\left(2\right)\right\}$
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, $x=\frac{P\oint s-20}{25}$
$\frac{P\oint s-40}{20}=\frac{P\oint s-20}{25}$

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,
$X+Y=100⇒$ equation(1)
$17X+12Y=1550⇒$ equation(2)
multiplying by 12 in equation(1) and the result subtract from equation(2)
$\left(17X+12Y\right)-\left(12X+12Y\right)=1550-12×100$
$5X=350$
$X=70$ (Number of graphic calculator)
Putting the value of X in equation (1)
$70+Y=100$
$Y=30$ (number of Scientific calculator)
Step 4
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 $=30$

RizerMix

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