Question 304318
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 = {{{40/.5}}}
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