Question: United Telephone charges a base rate of $10.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
- 2 minutes
- 10 minutes
- 20 minutes
- 40 minutes
- 60 minutes
Correct Answer: D
Solution and Explanation
Approach Solution 1:
Given in the question, United Telephone charges a base rate of $10.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute.
It has asked for what number of minutes the would the bills for each company will be same.
To solve this question let us assume that the number of minutes for a phone call is x
If someone talks for x minutes on United Telephone company then the charges will be = $10.00 + $0.25 *x
If someone talks for x minutes on Atlantic Call company then the charges will be = $12.00 + $0.20 *x
It has asked that after how many minutes the price of both phone call will become same.
So,
10.00 + 0.25x = 12 + 0.20x
Taking 0.20x to the left hand side and 10 to right hand side,
0.25x - 0.20x = 12 - 10
0.05x = 2
X = 2/0.05 = 40
Therefore after talking for 40mins both the company will charge the same amount.
Approach Solution 2:
Let x = the number of minutes used
United Telephone charge = $10.00 + $0.25x
Atlantic Call charge = $12.00 + $0.20x
For what number of minutes would the bills for each telephone company be the same?
In other words, for what value of x does $10.00 + $0.25x EQUAL $12.00 + $0.20x?
Let's find out....
10.00 + 0.25x = 12.00 + 0.20x
Subtract 10 from both sides to get: 0.25x = 2 + 0.20x
Subtract 0.20x from both sides to get: 0.05x = 2
Solve: x = 2/0.05 = 40
ASIDE: If you're not crazy about dividing by decimals, you can always take 2/0.05 and create an EQUIVALENT fraction first.
Take: 2/0.05
Multiply top and bottom by 100 to get: 200/5, which equals 40
Approach Solution 3:
United Telephone Total Charges = Base rate ($10) + 0.25* No. of Minutes
United Telephone Total Charges = Base rate ($12) + 0.20* No. of Minutes
For both of them to be same
($10) + 0.25* No. of Minutes = ($12) + 0.20* No. of Minutes
i.e. 0.05*No. of Minutes = 12 - 10 = 2
i.e. No. of Minutes = 40
“United Telephone charges a base rate of $10.00 for service, plus an”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT All the Quant”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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