SOLUTION: (substitution method word problem): One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced, wheras a second machine has a fixed daily cost of $10
Question 304318: (substitution method word problem): One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced, wheras a second machine has a fixed daily cost of $10 and a variable cost of $2 per item produced. Using y to represent the total daily costs of these items, determine the number of items x for which the total daily costs will be the same. What is the total daily cost for this number of items? (Use substitution method and steps would be appreciated) Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced,
wheras a second machine has a fixed daily cost of $10 and a variable cost of $2 per item produced.
Using y to represent the total daily costs of these items, determine the number
of items x for which the total daily costs will be the same.
What is the total daily cost for this number of items?
:
Write an equation for each statement:
"One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item"
y = 1.50x + 50
:
"a second machine has a fixed daily cost of $10 and a variable cost of $2 per item"
y = 2x + 10
:
determine the number of items x for which the total daily costs will be the same.
2nd machine cost = 1st machine cost
2x + 10 = 1.50x + 50
2x - 1.50x = 50 - 10
.5x = 40
x =
x = 80 items the cost for each machine is the same
:
What is the total daily cost for this number of items?
Substitute 80 for x in each equation
y = 1.50(80) + 50
y = 120 + 50
y = $170 daily cost, 1st machine
prove this using the 2nd equation
y = 2(80) + 10
y = 160 + 10
y = $170 daily cost using the 2n machine
