Question 100674
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.

{{{TR = 12x}}}, which is the total revenue.

{{{TC = 20 + 8x}}}, which is the total cost.

{{{P = 100}}}, which is the desired profit.

{{{P = TR - TC}}}, which is the standard profit equation.

Therefore, by substituting what we know:

{{{ 12x - (20 + 8x) = 100}}}.

Simplifying, we have:

{{{4x = 120}}}, so {{{x = 30}}}.

ALWAYS check your answer! So TR = 30*$12 = $360; TC = 20 + $8*30 = $260; which means P = 360 - 260 = 100. Check.