Welcome to a lesson on problem solving
using whole numbers. Here are some general guidelines for problem solving.
Number one, we need to read and understand the given information
as well as the question, and this often takes reading the problem several times.
Number two, we make a plan to solve the problem and if appropriate we should
sketch a diagram.
Then we'll solve and check our answer. And then we should also consider alternative
approaches.
Let's take a look at our first example. You're driving along I-10 and notice a
mileage marker
that reads one hundred twenty-seven. Then about thirty minutes later
you notice another mileage marker that ready one hundred fifty-four.
How far have you traveled? So you're in your car,
and you pass one mileage marker the reads
one hundred twenty-seven, and then later on in your trip
you pass another mileage marker that reads one hundred fifty-four.
And the question is, how far have you traveled? So we're going to determine what's the distance from
one hundred twenty-seven to one hundred fifty-four.
If it's not clear on how to approach this, you might want to take a look at a number line,
and consider two numbers that are much closer together. Let's say we want to
determine the distance from one to four.
Well if we're at one, and we traveled to four, that would be one,
two, three units. So four is three units
from one. But instead of counting each unit, what we could do is take the
ending value and subtract the beginning value
to give us the distance between the two points. So going back to our problem
we want to subtract
one hundred twenty-seven from one hundred fifty-four.
So we'll go ahead and set this up vertically, we'll have one hundred fifty-four
minus one hundred twenty-seven. Now we'll start on the right side,
four minus seven, we can't do that because four is too small.
So we'll borrow from the five, this will be a four,
and we'll add ten to the ones column, so we'll have fourteen minus seven,
that'll give us seven, and then four minus two is
two, one minus one is zero. So your car has traveled twenty-seven miles
Now let's say you read the back of a candy bar and it shows
each serving has twenty-four grams of sugar. If the candy bar contains three servings,
how much sugar is in the candy bar? And there are a couple of ways to approach this.
Well if there are twenty-four grams of sugar per serving, and there are three servings in
the candy bar,
we could just find this sum.
Let's go ahead and do that. Four plus four, plus four, that would be twelve,
carry that one. One plus two,
plus two, plus two, that would be seven. So there are seventy-two grams of sugar in this
candy bar.
Another way to solve the same problem would be to take twenty-four grams and multiply it
by three,
because there are three servings. Three times four would be twelve, carry the one.
Three times two is six, plus one, so again we have seventy-two grams.
So one method is not better than the other, however if there were
additional servings it may be easier to perform multiplication
rather than repeated addition. In this problem a stadium bleacher contains
forty-two rows,
with each row having sixty-four seats. How many seats are there?
So we have the set of bleachers, looks maybe something like this,
where there are forty-two rows.
So here we'd have forty-two rows, and each row
has sixty-four seats. So if we're going to divide this up in his direction,
there would be sixty-four seats
along here. If we're not sure how to approach
this, we could take a look at a simpler problem meaning what if we had
a smaller bleacher where there were two rows and three columns.
We could actually divide this up and determine the total number of seats.
There's two rows and then there's three columns.
We can see there's a total of six seats. An easier way to obtain that total would be
two times three equals six. So in our problem to determine the total number of seats
we'll take forty-two,
and we'll multiply it by sixty-four rather than adding sixty-four, forty-twos,
or forty-two sixty-fours. So we'll have four times two thats eight,
four times four would be sixteen. And now we multiply by the six, we're really multiplying by sixty, so we
have to add a zero to the ones column,
and then multiply by six. So six times two is twelve,
carry the one. Six times four is twenty-four, plus one
is twenty-five. And now we'll add, so we'll have eight here,
eight here, six and two. So the bleachers contain
two thousand, six hundred eighty-eight seats.
Now let's say that this year you have been able to raise one hundred fifty-eight dollars more
for your favorite charity than last year. If you raised four hundred twenty-seven dollars
last year for your charity,
how much did you raise this year? So we had four hundred twenty-seven dollars last year.
Our goal is to determine the amount this year,
given that we know that it's going to be one hundred fifty-eight dollars more then last year.
So we'll have to find the sum of these two dollar amounts. Four hundred twenty-seven
dollars plus one hundred fifty-eight dollars.
Start by adding the once place value. So we'll have fifteen, carry a one to the tens place value.
One plus two, plus five that's eight. Four four plus one is five.
So this year you will have raised five hundred eight-five dollars.
Now I think we have time for one more. Let's say you need to rent a moving truck.
If it cost twenty-two dollars per day and two dollars per mile,
how much will the rental cost be if you need the truck for three days,
and plan to drive a total of one hundred twenty miles. So here you have a fixed cost of twenty-two
dollars per day,
and then a variable cost, or a cost that varies based upon the amount you drive.
So if you need the truck for three days, twenty-two dollars for the first day, twenty-two
dollars for the second day,
and twenty-two dollars for the third day. We also could have just found the product of
twenty-two and three.
So here's the fixed cost, we'll have six
and six, so sixty-six dollars is our fixed cost.
And now we have the mileage cost,
and we plan to drive one hundred twenty miles at two dollars per mile.
So to find the mileage cost, it's probably going to be easier if we take
one hundred twenty and multiply it by two dollars
to determine the mileage cost. So two times zero is zero,
two times two is four, and two times one is two.
And again this is the variable cost because it varies based upon
how much we drive. So the total cost would be the sum of these two amounts.
Let's go ahead and line this up vertically. Sixty-six
plus two hundred forty, notice how we're lining up the place values.
So we have six in the ones, here we have a ten in the tens column, so we add a zero,
and carry a one. So the total cost to rent this vehicle
is going to be three hundred and six dollars for the three days
if you drive one hundred twenty miles.
I hope you found this video helpful.