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
RELATED QUESTIONS
a doughnut shop has a fixed cost of $124 per day and a variable cost of $.12 per... (answered by rfer)

A donut shop has a fixed cost of $124 per day and a variable cost of $0.12 per donut.... (answered by josgarithmetic)

a doughnut shop has a fixed cost of $124 per day and a variable cost of $.12 per... (answered by MathLover1)

Here is my question: The cost of producing a number of items x is given by C = mx + b,... (answered by funmath)

I am really lost on this question on how to go about this correctly: 50. Business and... (answered by Earlsdon)

THE COST OF PRODUCING A NUMBER OF ITEMS x IS GIVEN BY C = mx + b, IN WHICH b IS THE... (answered by Fombitz)

Suppose a company has fixed costs of $41,600 and variable cost per unit of 2 5 (answered by richwmiller)

I am not sure I am working this problem correctly could I please get some help on this... (answered by THANApHD)

The manager of a company manufacture surfboard has fixed costs (at o output)$500 per day... (answered by gonzo)