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?

A. 2 minutes
B. 10 minutes
C. 20 minutes
D. 40 minutes
E. 60 minutes


Solution -

Lets take number of minutes x .

Given that, 10+0.25x=12+0.2x ->0.05x=2 -> x=40minutes

ANS D

Thanks
Kudos Please

METHOD-1

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

Answer: Option D

METHOD-2

Just look at the difference the difference of $0.05 (0.25-0.20) for 'n' calls must bridge the difference of Base rate of $2 ($12- $10)

i.e. 0.05*n = 2

i.e. n = 40

Answer: Option D
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suppose x = no. of minutes

so ,
10 +0.25x = 12 +0.20x

Solving we get , x=40 mints

Answer D

Let # of minutes =x
So we have 10 +0.25x=12+0.2x

Solving above equation we get, x=40 min

Hence answer is D
Thanks,

MANHATTAN GMAT OFFICIAL SOLUTION:

Let x = the number of minutes.
A call made by United Telephone costs $10.00 plus $0.25 per minute: 10 + 0.25x.
A call made by Atlantic Call costs $12.00 plus $0.20 per minute: 12 + 0.20x.

Set the expressions equal to each other:
10 + 0.25x = 12 + 0.20x
x = 40

Answer: D.
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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

Answer: D

Cheers,
Brent
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We can let n = the number of minutes and create the equation:

10 + 0.25n = 12 + 0.2n

0.05n = 2

n = 40

Answer: D
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