Please help me with this Geometry problem?

The cost of a taxi ride is $2 for the first 1/5 mile and $.30 for each additional 1/5 mile. From 8pm to 6am there is a $.50 surcharge added to the cost of the ride after the first 1/5 mile. If Elizabeth got into a taxi at 9:05pm and paid $7.60, how far did she ride to the nearest 1/5 mile?

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  • 1 decade ago
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    Sounds like an algebra problem but there's no need for me to be picky. ;)

    Since Elizabeth spent a lot of money, let's assume she traveled more than just 1/5 mile.

    First lets consider the initial cost of the ride. $2 for the first 1/5 mile. But since Elizabeth gets into the taxi at around 9pm, this is between the 8pm to 6am period where there is an extra $0.50 surcharge. Therefore the cost for the first 1/5 mile is $2.50

    Next we'll use the letter N to represent the number of "1/5 miles" she traveled after the first 1/5 mile.

    Every 1/5 mile after the first costs Elizabeth $0.30. To determine how much she spends after the first 1/5 mile, all we have to do is multiply the number of 1/5 miles after the first (which we decided to call "N") by the price. So that part of the trip costs Elizabeth $0.30 x N.

    If we add what she paid for the first 1/5 mile to what she paid for the rest of the ride, we get the total cost of the ride, $7.60.

    Mathematically speaking:

    $First 1/5 + $Rest of trip = $Total

    $2.50 + $0.30 x N = $7.60

    Now solve the equation for N. Subtract $2.50 from both sides.

    $0.30 x N = $5.10

    Divide both sides by $0.30

    N=17

    That is 17 "1/5 miles" that she travels AFTER the first 1/5 mile. Therefore the total distance she travels is 18 "1/5 miles" if we add the first 1/5 mile in.

    I assume your teacher doesn't want 18 "1/5 miles" as an answer so we'll need a numerical value. Just multiply 18 by 1/5 to get a total number of "whole" miles.

    18 x 1/5

    =3.6 miles

    =3 and 3/5 miles

    Well I'm guessing that in the time it took me to type all that, two or three other people have probably already answered. Oh well.

    Edit: It also seems that there is confusion about whether to add the surcharge for every 1/5 mile after the first or just to the total cost. Your problem statement says "there is a $.50 surcharge added to the <i>cost of the ride</i>" so I assume it's just the total cost. If I am right, your answer is 3 and 3/5. If I am wrong, your answer is 1 and 2/5 like so many other people have suggested.

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  • 1 decade ago

    First thing you need to do is break apart the equation and define variables. Look for what's important in the word problem.

    The distance is unknown so use a variable

    The total 1/5's after the 1st mile= x

    The rates

    rate 1 = $2 for the 1st 1/5 of a mile

    rate 2 = $0.30 for every 1/5 mile AFTER the 1st one.

    rate 3 = $0.50 surcharge for every 1/5 mile EXCEPT the 1st one.

    The total = $7.60

    First... do you use the surcharge?

    Well Elizabeth got into the cab after 8pm so the answer is yes.

    That means that you now have enough information to set up the equation.

    2{The 1st 1/5} + x{remaining 1/5's} * (0.30 {Rate 2} + 0.50 {Rate 3}) = 7.60

    Which cleaned up looks like this...

    2 + x*(0.30 + 0.50) = 7.60

    Combine what's in the parentheses...

    2 + x*(0.80) = 7.60

    Subtract 2 from each side...

    2 - 2 + x*(0.80) = 7.60 - 2

    then divide each side by x's coefficient...

    x*(0.80) / 0.80 = 5.60 / 0.80

    Gives you x...

    x = 7

    Check it to make sure it works by substituting seven into the problem for the variable x...

    2 + 7*(0.80) = 7.60

    2 + 5.60 = 7.60

    7.60 = 7.60

    It works.

    That means that Elizabeth drove seven 1/5 miles or 1 & 2/5 miles.

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  • 1 decade ago

    This is a real life example. Why not do it by mental math?

    First, subtract the first 1/5 mile charge and the surcharge from the total $7.60.

    $7.60 - $2 - $0.50 = $5.1

    Since each additional (1/5) mile charge is $0.30, $0.3 goes into $5.1 17 times, which means the total miles should be 18(1/5) miles.

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  • raj
    Lv 7
    1 decade ago

    the amount Elizabeth paid=$7.60

    less the night surcharge=$7.10

    less $2 for the first 1/5 thmil2=$5.10

    divided by the tariff per mile=17

    so her ride was for 18*1/5=3 3/5 mile

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  • 1 decade ago

    ok first you subtracted the $2 leaving $5.60. Since it is after 8pm it is $.80 a 1/5 mile. so divide the $5.60 by $.80 and you get...7. so She went 7/5 or 1 2/5 of a mile.

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  • 1 decade ago

    7.60 - 2.00 = 5.60 1/5 mile

    5.60 - .50 = 5.10 1/5 + surcharge

    5.10 - .30x = 0.00

    .30x = -5.10

    x = -17 (cant have negative mileage)

    x = 17 1/5s of a mile

    17 * .2 (1/5) = 3.4 3.4 extra miles

    3.4 + .2 = 3.6 = 3 3/5 miles

    she rode 3 3/5 miles

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