Explore: Solving for the Unknown

In this unit, we're talking about the process of problem definition. One application of this concept is related to what you have traditionally known as "word problems" or "story problems." Working a word problem is just redefining the problem, or translating it, from words to Math. Math is a powerful problem solving tool.

1.?What number when added to 5 gives you 15?
?Another way to write this is: x + 5 = 15
?How did you solve the problem originally? Did you start by trying 1, then 2, then 3, etc.?
?You also can subtract 5 from both sides of the equal sign and end with x = 15 - 5 or x = 10.

2.?What number when added to 51 gives you 121?
x + 51 = 121
What is x?

3.?What number when you subtract 6 from it gives you 2?
?Another way to write this is: x -6 = 2
?You can add 6 to both sides and end with x = 2 + 6 or x = 8

4.?What number when you subtract 138 from it gives you 56?
x - 138 = 56 What is x?

5.?You are given miles = 50 miles, time = 1 hour. How fast are you going?
Speed = 50 miles/1 hour or 50 miles/hour.
You are given initial velocity = 0 miles/hour (you are standing still) and final velocity = 50 miles/hour. You travel a total of 100 miles. How long did it take you (time)?

Use Δ x = 1/2(v0 +v)t, where Δ x is distance traveled, v0 is initial velocity, v is final velocity, and t is time. You want to find time, and you have values for the other items. Plug in your values, and solve for t.

6.?Using the same equation from #5, you have traveled 25 miles in 2 minutes and come to a standstill. What was your initial velocity? (Hint: This time, final velocity is 0 miles/hour.)

7.?Still using the same equation, you start at 10 miles/hour and accelerate to 100 miles/hour in 6 seconds. How far did you travel?