SOLUTION: Here is the problem. A parts person has to spend exactly $100 and must buy 100 parts. Good parts cost 5$, regular parts cost 1$, and cheap parts cost 25 cents. He has to buy 100

Question 67717: Here is the problem. A parts person has to spend exactly $100 and must buy 100 parts. Good parts cost 5$, regular parts cost 1$, and cheap parts cost 25 cents. He has to buy 100 parts for $100 and have some of each part. I tried the trial and error method and got an answer, but wanted to get an anwer algebraically, (sp?)
I tried: 5x + y + .25z = $100
x + y + z = 100 and substituting variables but could not get it to work. I appreciate your help.
George
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A parts person has to spend exactly $100 and must buy 100 parts. Good parts cost 5$, regular parts cost 1$, and cheap parts cost 25 cents. He has to buy 100 parts for $100 and have some of each part.
:
Let the three types of parts = x, y, z
Three unknowns, two equations calls for some assumptions
:
We know that the $5 part (x) has to be 4 or less,
lets assume x = 3 good parts at $5 ea
:
3 + y + z = 100
y + z = 97
and:
3(5) + y + .25z = 100
15 + y + .25z = 100
y + .25z = 85
:
See if these two equations will give an integer answer for z
y + z = 97
y + .25z = 85
-------------- subtract
.75z = 12
z = 12/.75
z = 16 ea cheap parts
Find y from the equation y + z = 97
y + 16 = 97
y = 97 - 16
y = 81 ea regular parts
:
we have 3 good, 81 regular and 16 cheap parts
:
Check in the cost equation:
3(5) + 81 + .25(16) =
15 + 81 + 4 = $100

RELATED QUESTIONS
Three parts of liquid chlorine and two parts of salt are added to each 100 parts of water (answered by josmiceli,ikleyn)

Angela made some compost using 1 part coffee grounds, 6 parts food waste, 12 parts... (answered by richwmiller)

Rory, Leo, and Joey win $362 880 in a lottery. They decide to divide the winnings so... (answered by addingup)

A shipment of assembly parts from a vendor offering inexpensive parts is used in a... (answered by Boreal)

A shipment of assembly parts from a vendor offering inexpensive parts is used in a... (answered by ikleyn)

how to divide 100 into two parts so that the difference between the two parts is 5 ? i... (answered by richard1234)

Your washing machine has stopped working. Acme Repair charges $100 for a service call... (answered by nerdybill)

Your washing machine has stopped working. Acme repair charges $100 for a service call... (answered by solver91311)

In this exercise they want you to find the percent, parts out of 100, decimal and/or... (answered by checkley77)