SOLUTION: hello i have 2 questions. A mechanics hourly wage is 4 times her helpers. They were paid a total of 208$ for a job on which the mechanic worked 5 hours and the helper worked 6 h

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Question 487759: hello i have 2 questions.
A mechanics hourly wage is 4 times her helpers. They were paid a total of 208$ for a job on which the mechanic worked 5 hours and the helper worked 6 hours. Find the hourly wage of the helper.
A postal clerk sold a total of 25 stamps for 10.80. Some were worth 40cents and others were worth 45cents. Find the number of each sold.
it would be great if you guys also showed me the work so I can understand how to answer these questions.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
first problem:
a mechanic's hourly wage is 4 times the helper's.
total job paid $208.
mechanic worked 5 hours and the helper worked 6 hours.
let x = the helper's pay per hour.
then 4x = the mechanic's pay per hour.
general formula used is hourly wage * number of hours to do the job = total cost of the job.
let r = hourly wage and t = number of hours to do the job and c = total cost of the job and the formula becomes:
r * t = c
the hourly wage is x for the helper and 4x for the mechanic.
the total cost of the job is $208.00
the time required to do the is 5 hours for the mechanic and 6 hours for the helper.
the formula becomes:
(4x * 5) + (x * 6) = $208.00
this becomes:
20x + 6x = $208.00 which becomes:
26x = $208
divide both sides of this equation by 26 to get:
x = $208.00 / 26 = $8.00
the helper's hourly wage is $8.00 per hour.
the mechanic's hourly wage is $32.00 per hour.
5 * 32 = $160.00
6 * 8 = $48.00
$160.00 + $48.00 = $208.00

second problem:
25 stamps sold for $10.80
some were worth 40 cents
some were worth 45 cents
how many of each were sold.
total sold was 1080 cents
x is the number of 40 cent stamps that were sold.
y is the number of 45 cent stamps that were sold.
x + y = 25
this means that the total of x and y stamps came out to be 25.
40x + 45y = 1080
this means that the total money from 40 cent stamps and the total money from 45 cent stamps equaled a total of 1080 cents .
you need to solve these 2 equations simultaneously to get your answer.
you can do that by substitution or elimination or by graphing.
we'll do it by elimination so you can see how that process works.
your equations are:
x + y = 25 (equation 1)
40x + 45y = 1080 (equation 2)
multiply both sides of equation 1 by 40 to get:
40x + 40 = 1000 (equation 3 which equals equation 1 multiplied by 40)
40x + 45y = 1080 (equation 2)
subtract equation 3 from equation 2 to get:
5y = 80
divide both sides of this equation by 5 to get:
y = 16
substitute for y in equation 1 to get:
x + 16 = 25
subtract 16 from both sides of this equation to get:
x = 9
your answer should be:
x = 9
y = 16
this means that:
the number of 40 cent stamps is 9.
the number of 45 cent stamps is 16.
substitute these values for x and y in the second equation to get:
40x + 45y = 1080 becomes:
40*9 + 45*16 = 1080 which becomes:
360 + 720 = 1080 which becomes:
1080 = 1080
this confirms the values for x and y are good.
both equations have been solved simultaneously which means the same value of x and the same value of y is a solution to both equations.
that's your answer.
number of 40 cent stamps is equal to 9.
number of 45 cent stamps is equal to 16.