Originally Answered: I have trouble solving these kind of problems?
1. Just translate English into Algebra:
"r is twice the value of p" ==> r = 2p
"p is 8 less than s" ==> p = s - 8
Since p = s - 8, then s = p + 8. You can get this by remembering "families of facts" from grade school, or using algebra by adding 8 to both sides of p = s - 8.
So, since r = 2p and s = p + 8, then
r + s = 2p + (p + 8)
r + s = 3p + 8
2. This is an old brainteaser. Since the trains are heading at each other, the relative speed between them is 55 mph + 35 mph = 90 mph. At 90 mph, how long does it take to close the 337.5 mile gap between them?
The straight-arrow approach is that after x hours, train A is
a = 55*x miles
from Romeoville. Train B is
b = 337.5 - 35*x miles
away from Romeoville. When the trains meet, a=b, or
55x = 337.5 - 35x
90x = 337.5
and then solve for x to find that you have the same answer as before.
3. Let x peanut butter jars bought. Mike spent 8*$2 on the 8 jelly jars and x*$4 on peanut butter. This totals:
16 + 4x = 28
Solve this for x. Remember units: x is measured in "jars" or "jars of peanut butter".
4. First, look at the times. Let t be the walking time to school. Since the round-trip time is 8 hours (just who spends 8 hours/day walking to/from school, anyway?!?!), the return time is (8-t) hours. But the return time (8-t) is 2 hours longer than t, so:
8 - t = t + 2
6 = 2t
t = 3
It took 3 hours to school and (8-3) = 5 hours to return.
Next, use (distance) = (speed)*(time) for each trip to make two equations:
d = (5 mph)*(3 hours) .... distance traveled on first trip is 5*3 = 15 miles
15 = (x mph)*(5 hours)
15 = 5x
x = 15/5 = 3 mph
5. Read carefully. The problem is asking for the cost per cup of coffee. In this problem d dollars worth of coffee makes c cups of brewed coffee. The cost per cup is d/c. It's *already* in terms of c and d. The most important strategy is to read the question carefully.
Above are some strategies, mostly in the examples, of how to solve problems like these.