SOLUTION: I have two word problems that I really need help on. 1)Two cars leave Denver at the same time and travel in opposite directions. One car travels 15mi/h faster than the other car.

Question 100674: I have two word problems that I really need help on.
1)Two cars leave Denver at the same time and travel in opposite directions. One car travels 15mi/h faster than the other car. The cars are 460mi apart in 4 hours. How fast is each car traveling?
2)A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. How many T-shirts does the club need to make and sell in order to earn $100?
I was wonder how can we contact the tutors to thank them for helping us?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
1) Problems like this build on the fact that something has to equal something else. In this case, we know they both traveled for 4 hours. The distance equation is d = r * r, so for Car1 d1 = r*4 and for Car2 d2 = (r+15)*4. And we know that d1 + d2 = 460 miles (the distance they are apart after 4 hours). Substituting, we have 4r + 4r + 60 = 460. That simplifies to 8r = 400, so r = 50. That means r+15 is 65. Car1 traveling at 50 and Car2 is traveling at 65.
ALWAYS check your answer. 4*50 = 200 miles. 4*65 = 260. 200+260=460. Check.
2) Total Revenue = $12 times the number of shirts sold (call that x). Total Cost is $20 plus $8 * x. Profit is total revenue minus total cost. So, we now have some linear equations to solve, with only one variable.
, which is the total revenue.
, which is the total cost.
, which is the desired profit.
, which is the standard profit equation.
Therefore, by substituting what we know:
.
Simplifying, we have:
, so .
ALWAYS check your answer! So TR = 30*$12 = $360; TC = 20 + $8*30 = $260; which means P = 360 - 260 = 100. Check.
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