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

kloseyq 2021-12-18 Answered
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)
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Expert Answer

Thomas Nickerson
Answered 2021-12-19 Author has 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
25m20m=4020
5m=20
m=4 minutes so after 4 minutes Mona ahead Ahmed
2) 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)=155012100
5x=15501200
5x=350
x=70
y=10070=30
graphic calculators sold =70
scientific calculators sold =30
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lenkiklisg7
Answered 2021-12-20 Author has 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 =$17
Selling price of scientific calculator =$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=Points4020{equation(1)}
For Mona;
Points =20+25×minutes
Minutes=Points2025{equation(2)}
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=Ps4020
Also, x=Ps2025
Ps4020=Ps2025
25 Points1000=20 Points400
25 Points20 Points=1000400
5 Points=600
Points =120
Putting these points in equation (1) or equation(2), then we get the minutes until Mona overtakes Ahmed.
Minutes=Points2025
=1202025
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)
(17X+12Y)(12X+12Y)=155012×100
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=Points4020
For Mona;
Minutes=Points2025
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

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RizerMix
Answered 2021-12-28 Author has 438 answers
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
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