By the end of this lesson the student will be able to:
set up an equation that "matches"
in numbers what the puzzle expresses in words.
Assignment: Completion or review
of Basic Algebra - Lesson
In the last lesson, you learned
to balance an equation, making what is on one side of the equal sign equal
to what is on the other side. In other words, the left member and the right
member of the equation "balance."
Examples of equations:
5 + 7 - 2 = 2(5) (the answer on the
left side is 10 and the answer on the right side is 10)
100/25 = 347 - 343 (the answer is
4 on the left of the equal sign and 4 on the right also)
You also learned to isolate variables.
Equations involving unknown variables are solved by balancing the left
member and the right member. In the equation, y + 5 = 12, the proper procedure
in solving for y is to "isolate" y. This means we want y to stand by itself
on one side of the equal sign.
Now, keep in mind that we want every
thing to "balance" on either side of the equal sign. This means whatever
I do to the left member, I must do to the right member. So, to isolate
y and solve the equation, I must "move" the 5 to the other side of the
equal sign. To do this, I must make it zero on the left side of the equation
by subtracting 5:
y + 5 = 12
y + 5 - 5 = 12 - 5
y + 0 = 12 - 5
y = 7
Equations can also be used to solve
puzzles. You must set up an equation that "matches" in numbers what the
puzzle expresses in words. Then, solve for the variable. That will be the
answer to the puzzle.
Why don't you try a few?
including Answer key:
1. Farmer Brown told Bob and Sue
that they could pick apples from his tree, but that neither of them could
take more than 20. They worked for a while, and then Bob asked Sue, "Have
you picked your limit yet?"
Sue replied, "Not yet. But if I
had twice as many as I have now, plus half as many as I have now, I would
have my limit." How many did Sue have?
2. A little boy was told not to eat
the grapes from the vine for fear that he would eat too many and get a
stomachache. Sneaking out to the grape arbor when his mother wasn't looking,
the little boy ate grapes for five days, each day eating 6 more than the
day before. In fact, after five days, the little boy was so sick that he
had to confess to his mother that he had eaten 100 grapes. How many grapes
did the little boy eat on EACH of the five days?
3. How high is a tree that is 15
feet shorter than a pole three times as tall as the tree?
1. Let x = the number of apples she had.
2x + 1/2 x = 20
as a fraction with 2 as the denominator would be written 4x/2.)
4x/2 + 1/2 x = 20
5x/2 = 20
5x/2 X 2 = 20 X 2
5x = 40
5x/5 = 40/5
x = 8 apples
2. Let x = number of grapes the little boy ate the first day
x + 6= number of grapes eaten the second day
x + 6 + 6 = number of grapes eaten the third day
x + 6 + 6 + 6 = number of grapes eaten the fourth day
x + 6 + 6 + 6 + 6 = number of grapes eaten the fifth day
Five days' worth of grapes = 100
in all. Therefore, the equation to set up is:
x + (x + 6) + (x + 6 + 6)
+ (x + 6 + 6 + 6) + (x + 6 + 6 + 6 + 6) = 100
x + x + 6 + x + 12 + x + 18 + x + 24 = 100
5x + 60 = 100
5x + 60 - 60 = 100 - 60
5x = 40
5x/5 = 40/5
x = 8 grapes eaten on the first day
(Now put 8 in place of x in all the other expressions.)
x + 6 = 14 grapes eaten the second day
x + 6 + 6 = 20 grapes eaten the third day
x + 6 + 6 + 6 = 26 grapes eaten the fourth day
x + 6 + 6 + 6 + 6 = 32 grapes eaten the fifth day
(To check, add 8, 14, 20, 26, ad 32. They equal 100.)
3. Let y = number of feet in height of tree
3y would equal the number of feet in height of the pole
Set up the equation:
y = 3y - 15
y - 3y = 3y - 3y - 15
-2y = -15
-2y/-2 = -15/-2
y = 7.5 feet
3y = 22.5 feet
Algebra Lesson 8