SOLUTION: Hello, I would like to make sure I have set-up the equation correctly for the two following word problems: A factory had fixed costs of $12000 per month and a unit cost of $3.7

Question 227802: Hello,
I would like to make sure I have set-up the equation correctly for the two following word problems:
A factory had fixed costs of $12000 per month and a unit cost of $3.75 for every pair of ice grippers that it makes. If the factory can sell all the ice grippers it can make for $8.75 per pair, how many must be sold per month for the factory to break even?
Is the equation? 3.75+8.75x=12000
Number 2... Sally and Mark are having a friendly race with their scooters. Their scooters took off at the same time. Sally was able to go 30mph all the way to the finish line but Mark averaged only 20mph. When Sally finished, Mark still had 7.5 miles to go. How far was the finish line from the start?
Is the equation? 20+ 7.5x= 30-x
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A factory had fixed costs of $12000 per month and a unit cost of $3.75 for every
pair of ice grippers that it makes. If the factory can sell all the ice grippers
it can make for $8.75 per pair, how many must be sold per month for the factory to break even?
:
Is the equation? 3.75+8.75x=12000
no
Cost = 3.75x + 12000
Revenue = 8.75x; (total from sales)
Break even occurs when Rev = cost, therefore find x from:
8.75x = 3.75x + 12000
8.75x - 3.75 = 12000
5x = 12000
x = 2400 has to be sold to break even
:
You confirm this by checking (are they equal?):
8.75(2400)
and
3.75(2400) + 12000
:
:
Number 2... Sally and Mark are having a friendly race with their scooters.
Their scooters took off at the same time.
Sally was able to go 30mph all the way to the finish line but Mark averaged only 20mph.
When Sally finished, Mark still had 7.5 miles to go.
How far was the finish line from the start?
:
Is the equation? 20+ 7.5x= 30-x
no
:
Sally's time to go the distance = Marks time to go 7.5 less than the distance.
time = dist/speed
=
Cross multiply
30(x-7.5) = 20x
30x - 225 = 20x
30x - 20x = + 225
10x = 225
x = 22.5 miles
;
:
Check this by finding if the time to go 22.5 mi at 30 mph,
Is the same as going 15 mi at 20 mph
22.5/30 = .75 hr
15/20 = .75
;
:
Did this make sense to you, any questions?
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