Maths-
General
Easy
Question
When Apple sells their iPads, they increase the price $50 from what it costs them to actually make the iPads. One Apple store sold 10 iPads one day which cost a total of $5000. How much does an iPad cost to actually make?
Hint:
- Hint:
○ Form the eqaution using given information.
○ Take variable value as any alphabet.
○ Take terms with cofficient at one side and without cofficients at another side.
The correct answer is: $450.
- Step by step explanation:
○ Given:
Increase in price= $50.
Total no. of iphone sold = 10
Total cost of iphone = $5000.
○ Step 1:
Let cost of making iphone be x months.
So,
Cost of 1 iphone = cost of making + $50
Cost of 1 iphone = x + $50
Hence,
Cost of 10 iphone = (x + $50 ) 10
Cost of 10 iphone = (10x + 500 )
○ Step 2:
○ As total cost is $5000.
∴ 10x + 500 = 5000
10x = 5000 - 500
10x = 4500
x = ![4500 over 10](data:image/png;base64,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)
x = 450
- Final Answer:
Hence, cost of making of iphone is $450.
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Prove that ∠ ABC ≅ ∠ ADC
![](data:image/png;base64,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)
Prove that ∠ ABC ≅ ∠ ADC
![](data:image/png;base64,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)
Maths-General
Maths-
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
Maths-General
Maths-
Prove that ∠ ABC ≅ ∠ PQR
![](data:image/png;base64,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)
Prove that ∠ ABC ≅ ∠ PQR
![](data:image/png;base64,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)
Maths-General
Maths-
Show the conjecture is false by finding a counterexample. If
≅
, then point B is the midpoint of AB.
Show the conjecture is false by finding a counterexample. If
≅
, then point B is the midpoint of AB.
Maths-General
Maths-
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
Maths-General