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Thread: word problem: The base rate for the phone bill is $82.00 per month....

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    word problem: The base rate for the phone bill is $82.00 per month....

    Hi, my name is Eddy. I am struggling with this here word problem. I would appreciate any help which include steps and rationale behind the steps. thank you so much in advance.
    the base rate for a telephone bill for married couple is $82.00 per month.each member paid 1/2 of the bill plus their data usage. the total bill for the month was $125.00. what was he payment per person, if 60% of data usage was his?.

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    Quote Originally Posted by eddy2017 View Post
    Hi, my name is Eddy. I am struggling with this here word problem. I would appreciate any help which include steps and rationale behind the steps. thank you so much in advance.
    the base rate for a telephone bill for married couple is $82.00 per month.each member paid 1/2 of the bill plus their data usage. the total bill for the month was $125.00. what was he payment per person, if 60% of data usage was his?.
    So the combined data usage charge = 125 - 82 = 43

    How would split this bill?

    What are your thoughts?

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    [QUOTE=Subhotosh Khan;424627]So the combined data usage charge = 125 - 82 = 43

    How would split this bill?

    What are your thoughts?



    my try is not much:
    regular tariff> 82
    bill of the month> 125
    each member paid half> 62.50 (?)


    he has used up 60% of data usage = 60/100=0.6

    i was told the one equation i could set up was:
    data cost= his data cost+ her data cost
    but that doesn't give me the amount each one of them paid.

    what is 43 ?. what does this number represent. I am confused here.
    someone told me 43 is the data cost for the man. I don't get it. Sorry
    Last edited by eddy2017; 02-25-2018 at 08:34 PM.

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    [QUOTE=eddy2017;424631]
    Quote Originally Posted by Subhotosh Khan View Post
    So the combined data usage charge = 125 - 82 = 43

    How would split this bill?

    What are your thoughts?



    my try is not much:
    regular tariff> 82
    bill of the month> 125
    each member paid half> 62.50 (?)


    he has used up 60% of data usage = 60/100=0.6

    i was told the one equation i could set up was:
    data cost= his data cost+ her data cost
    but that doesn't give me the amount each one of them paid.

    what is 43 ?. what does this number represent. I am confused here.
    someone told me 43 is the data cost for the man. I don't get it. Sorry
    Do you see (and I have shown) that:

    total data usage bill = total bill - tariff


    total data usage bill = 125 - 82 = 43

    split it up 60-40 ratio - continue....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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    [QUOTE=Subhotosh Khan;424633]
    Quote Originally Posted by eddy2017 View Post
    Do you see (and I have shown) that:

    total data usage bill = total bill - tariff


    total data usage bill = 125 - 82 = 43

    split it up 60-40 ratio - continue....
    I'm sorry. I'm stuck there. I need to understand the process of how to go about setting up an equation using the data given. If you'd care to explain It would help me a lot understand the rational behind the setup

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    Quote Originally Posted by eddy2017 View Post

    I'm sorry. I'm stuck there. I need to understand the process of how to go about setting up an equation using the data given. If you'd care to explain It would help me a lot understand the rational behind the setup
    Name things.

    [tex]b = base\ rate[/tex].

    [tex]d = data\ usage\ cost.[/tex]

    [tex]h = husband's\ data\ usage\ cost[/tex].

    [tex]w = wife's\ data\ usage\ cost.[/tex]

    [tex]m = male's\ share\ of\ bill.[/tex]

    [tex]f = female's\ share\ of\ bill.[/tex]

    You have six unknowns so you need six pieces of information.

    [tex]b + d = 125.[/tex] Does that make sense?

    [tex]b = 82.[/tex] Where did that come from?

    [tex]d = h + w.[/tex] Why?

    [tex]h = 0.6d.[/tex] How do I know that?

    [tex]m = \left ( \dfrac{1}{2} * b \right ) + h.[/tex] Did that come from somewhere? Where?

    [tex]f = b + d - m.[/tex]

    Now start eliminating unknowns. This is purely mechanical. No thought required.

    [tex]b = 82 \text { and } b + d = 125 \implies 82 + d = 125 \implies d = 125 - 82 = 43.[/tex]

    [tex]f = b + d - m \text { and } b + d = 125 \implies f = 125 - m.[/tex]

    [tex]h = 0.6d \text { and } d = 43 \implies h = 0.6 * 43 = 25.80.[/tex]

    [tex]m = \left ( \dfrac{1}{2} * b \right ) + h = \left (\dfrac{1}{2} * 82 \right ) + 25.80 = 41 + 25.80 = 66.80.[/tex]

    [tex]f = 125 - m = 125 - 66.80 = 58.20.[/tex]

    Does that make sense?
    Last edited by JeffM; 02-25-2018 at 10:39 PM.

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    Quote Originally Posted by Denis View Post
    Eddy, are you a student attending math classes?
    No, I am prepping for a math test I have to sit to get a certificate in esol. I am learning many things on my own and thru different websites, but with word problems I do struggle.

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    word problem

    jeefm ,thank you so much. It does makes sense now. Thanks for taking the time to explain so well. and thanks to the others too.

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    word problem

    Quote Originally Posted by Denis View Post
    **** that is unclear, and should be stated this way:
    Each member pays their data usage plus 1/2 of the BASE RATE.

    Invoice would look like:
    Base rate....................82.00
    Month's data usage......43.00
    Total........................125.00

    husband: 82.00 / 2 + 60% of 43
    wife......: 82.00 / 2 + 40% of 43

    Jeff showed you that in more details.

    Good luck Eddy!


    thank you so much to all of you. Dennis, thanks for correcting the problem. yes, I thought there was something wrong with the structure. just one question to either you or Jeff
    after studying what Jeff so extensively explained, I can not figure out this
    82+ d = 125. (D ???)
    d= 12 why 12? what is the value of d?

    what is the value of m?

    f= b + d - m
    f = 125 - m. ( m?)

    and lastly, where did the 43 come from?

    h= 0.6 d(data usage cost)= 43( ?)
    h= 0.6 (man’s data usage)
    h= 0.6 * 43 = 25.80

    thank you so much for everything. I will continue to study hard, but I know you will have to keep on helping me. I like math but I struggle with a lot of deductions. it takes practice and a lot of thinking'.
    but I know I can count on you.
    this esol degree represent s a lot for me and my family. we are struggling financially and I have to ace that math test. got no other option, and have 10 months to take the math test.



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    Quote Originally Posted by eddy2017 View Post
    thank you so much to all of you. Dennis, thanks for correcting the problem. yes, I thought there was something wrong with the structure. just one question to either you or Jeff
    after studying what Jeff so extensively explained, I can not figure out this
    82+ d = 125. (D ???)
    d= 12 why 12? what is the value of d?

    and lastly, where did the 43 come from?



    No, d is not equal to 12. Just think about this practically, as though you were actually paying your phone bill. You get a bill. You know that the bill costs at least $82.00, which is the base charge just for having a phone at all (b). However, in this particular month the total bill has come out to more than that: $125. The difference between these two amounts ($125 - $82 = $43) is equal to the extra charges you had on your bill for this month (charges over and above the base rate). Since the only source of extra costs mentioned in the problem is data usage, you know that this $43 is how much extra you were charged on the bill for your data usage this month. That's where the d = $43 comes from.


    Quote Originally Posted by eddy2017 View Post
    what is the value of m?
    Quote Originally Posted by eddy2017 View Post
    f= b + d - m
    f = 125 - m. ( m?)


    As defined by JeffM, "m" is the man's share of the bill. Since the man and woman are splitting the bill, their two shares have to add up to the total bill amount:

    m + f = (b + d)
    <---- (total bill amount = base rate + data usage charges)

    Quote Originally Posted by eddy2017 View Post
    h= 0.6 d(data usage cost)= 43( ?)
    h= 0.6 (man’s data usage)
    h= 0.6 * 43 = 25.80


    The problem states that the husband's portion of the data usage was 60% of the total data usage, so he should pay 60% of d, which equals 0.6 times d.

    0.6 * $43.00 = $25.80

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