SOLUTION: Raina works as a tutor for $7 an hour and as a waitress for $12 an hour. This month, she worked a combined total of 97 hours at her two jobs. Let t be the number of hours Raina wo

Question 1193391: Raina works as a tutor for $7 an hour and as a waitress for $12 an hour. This month, she worked a combined total of 97 hours at her two jobs.
Let t be the number of hours Raina worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Found 3 solutions by Theo, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let x = the number of hours worked as a tutor
let y = the number of hours worked as a waitress.
let t = the total number of hours she worked during the month.
7x = the total amount of money she made as a tutor.
15y = the total amount of money she made as a waitress.
t = x + y means the total number of hours she worked during the month is the sum of the total number of hours she worked as a tutor plus the total number of hours she worked as a waitress during the month.
let d = the total amount of dollars she made during the month.
the formula for d becomes:
d = 7x + 15y
that's the equation for the total dollar amount she made during the month.
the expression to determine the total dollar amount she earned during the month is 7x + 15y.
that's the expression on the right side of the equation.

in answer to your request for a numeric solution, please read the following:

the problem does clearly state to "Write an expression for the combined total dollar amount she earned this month."
it does not ask for a numeric solution.

despite that, i don't believe this problem lends itself to a unique solution, the reason being that you have 2 equations in 3 unknowns.
your 3 unknowns are the number of hours worked at 7 dollars an hour and the number of hours worked at 15 dollars an hour and the total amount of money that was made.
you do know that the total hours worked is 97, but you don't know what the total amount of money that was earned is.
that is required, as far as i can tell, for there to be unique solution.
there are limits to the amount of money that can be earned, given the constraints of the problem.
the minimum money that can be earned is 7 * 97 + 15 * 0 = 679.
the maximum money that can be earned is 7 * 0 + 15 * 97 = 1455.
what this says is that she couldn't make less than 679 dollars and she couldn't make more than 1455 dollars, given that she worked 97 hours during the week at 7 dollars an hour for the tutor job and 15 dollars an hour for the waitress job.
if you pick any amount of money between these extremes, you can then solve for the number of hours worked at each.
for example, if you say that she made 1000 dollars during the week, then you can solve for the number of hours worked at each job as follows:
your equations become:
x + y = 97
7x + 15y = 1000
these are 2 equations that need to b solved simultaneously.
multiply both sides of the first equation by 7 to get:
7x + 7y = 679
7x + 15y = 1000
subtract the first equation from the second to get:
8y = 321
solve for y to get:
y = 321/8 = 40.125.
since x + y = 97, then y = 97 - 40.125 = 56.875
to confirm, replace x and y in the original equations to get:
x + y = 97 becomes 56.875 + 40.125 = 97 which becomes 97 = 97 which is true.
7x + 15y = 1000 becomes 7*56.875 + 15 * 40.125 = 1000 which becomes 1000 = 1000 which is true.
if the total amount of money earned is 1000, then the value of x and y will be 56.875 and 40.125 respectively.
given another value of money earned between 679 and 1455, you would get a different number of hours for x and y.
let me know if you have any further questions.
i'll answer to the best of my ability.
theo

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Raina works as a tutor for $7 an hour and as a waitress for $12 an hour.
This month, she worked a combined total of 97 hours at her two jobs.
Let t be the number of hours Raina worked as a tutor this month.
Write an expression for the combined total dollar amount she earned this month.
~~~~~~~~~~~~~~~~~

            Tutor @Theo misread the problem, so his writing is not what is required in the problem.

            I came to do the job in a way in how it SHOULD be done.

If Raina worked a combined total 97 hours at her two jobs and worked t hours as a tutor, then she worked (97-t) hours as a waitress. As a tutor, she earned 7t dollars; as a waitress, she earned 12*(97-t) dollars. In total, she earned 7t + 12*(97-t) dollars, combined. ANSWER. In total, Raine earned 7t + 12*(97-t) dollars.

Solved.

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In such simple problems, writing governing equations/equation is, usually, quite simple and routine task.
The standard mantra in doing such job is to say " write equation as you read the problem ".

Some tutors like to present such job as complicated high intellectual heroic job, but actually it is as simple as reading the problem.
It only requires attention while reading and a bit of common sense.

The student's goal is to learn on writing such equations AUTOMATICALLY.

Normally, each such problem can be done in 5 - 10 seconds.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
t, how many hours worked as tutor the month
97-t, how many hours worked as waitress

Money she earned this month: , and this can be simplified if you want.
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