SOLUTION: the material cost of a medical gadget is $4 less than twice the cost of the direct labour and the overhead is 5/6 of the direct labour cost. the total cost of the gadget is 157$ wh

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Question 186222: the material cost of a medical gadget is $4 less than twice the cost of the direct labour and the overhead is 5/6 of the direct labour cost. the total cost of the gadget is 157$ what is the amount of each of the three elements of cost?? "i had a hard time figuring this out and i have a lot of questions like this in college. Can you please show me all the steps thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
First, assign the unknowns and write an equation for each phrase
:
Let x = the material cost
Let y = cost of direct labor
Let z = overhead
:
"the material cost of a medical gadget is $4 less than twice the cost of the direct labour"
x = 2y - 4
:
"the overhead is 5/6 of the direct labour cost.
z = 5%2F6y
:
" the total cost of the gadget is 157"
x + y + z = 157
:
what is the amount of each of the three elements of cost
:
Note that x and z both have an relationship to y, if we substitute for x & z
in the total cost equation, we only have one unknown to deal with.
:
x + y + z = 157
:
(2y-4) + y + 5%2F6y = 157
:
2y - 4 + y +5%2F6y = 157
:
3y + 5%2F6y = 157 + 4
:
3y + 5%2F6y = 161
Get rid of that denominator, multiply equation by 6, results:
6(3y) + 5y = 6(161)
:
18y + 5y = 966
:
23y = 966
y = 966%2F23
y = $42 is the direct labor cost
:
We can use the 1st two equation to find x & z, substitute 42 for y:
x = 2y - 4
x = 2(42) - 4
x = 84 - 4
x = $80 is the material cost
:
z = 5%2F6y
z = 5%2F6(42)
z = 5(7); canceled 6 into 42
z = $35 is the overhead cost
;
:
Check solutions in the total cost equation
80 + 42 + 35 = 157
:
:
Try using this method on all your word problems. Even if you do not understand
the whole problem, you can write a simple equation for each statement. After
you have done that, a plan of attack will often be apparent to you.
Good luck Carl