In this video, we will solve an application problem
using a linear equation in one variable.
We will also be using the problem solving
strategy shown here below where
step one is to read the problem.
Step two, identify what you are looking for.
Three, name what you are looking for
and choose a variable to represent that quantity.
Four, translate into an equation.
Five, solve the equation.
Six, check the answer.
And finally, seven, answer the question
with a complete sentence.
Reading the problem, the first day of a water polo
tournament, the total value of tickets sold was $17,610.
One-day passes sold for $20
and tournament passes sold for $30.
The number of tournament passes sold was 37
more than the number of day passes sold.
How many day passes and how many
tournament passes were sold?
For this problem we are looking for the number of day passes
and the number of tournament passes that were sold.
So for this problem we do have two unknowns,
but because the number of tournament passes sold
was 37 more than the number of day passes sold,
lets let the variable D represent
the number of day passes sold.
And then because the number of tournament passes sold
was 37 more than the number of day passes sold,
we can use the expression D plus 37 to represent
the number of tournament passes sold.
Because the total value of all the tickets sold was $17,610,
let's now use this table here to come up with an expression
for the total value of the one-day passes
and the total value of the tournament passes.
So we know the number of one-day passes is represented
by the variable D, each one-day pass cost $20.
So the ticket value of each one-day pass is $20,
which means the total value of all of
the one-day passes is $20 times D or 20D.
And now, for the tournament passes, the number of tournament
passes is represented by the expression D plus 37.
The ticket value of each tournament pass is $30
which means the total value of all of the tournament passes
is $30 times the quantity D plus 37,
or just 30 times the quantity D plus 37.
And we know the value of all of the tickets sold
is $17,610, which we'll record here.
Now we have all the information we need to complete step
four which is to translate the information into an equation.
Using this last column, the value of the one-day passes
plus the value of the tournament passes must equal $17,610,
which gives us the equation 20D plus 30,
times the quantity D plus 37 equals $17,610.
The next step is step five.
To solve the equation, then step six is check the answer.
Finally step seven, answer the
question with a complete sentence.
Let's solve this equation on the next slide.
The first step is to simply both sides of the equation,
the right side does not simplify,
but the left side does.
We simplify the left side by clearing
the parenthesis and combining like terms.
Which means the next step is to distribute 30.
This gives us 20D, plus 30 times D is 30D,
plus 30 times 37 is 1,110.
Still simplifying the left side we combine like terms.
20D plus 30D is 50D, we have 50D plus 1,110 equals 17,610.
The next step is to add or subtract to isolate the
variable term and combine the constants on the other side.
To isolate 50D we need to undo plus 1,110,
by subtracting 1,110 on both sides of the equation.
Simplifying 1,110 minus 1,110 is zero.
The left side is now 50D equals, on the right side,
17,610 minus 1,110 is 16,500.
Now that we've isolated the variable term,
the next step is to multiply or divide to isolate
the variable and solve for D.
Because 50D means 50 times D, to undo the multiplication
and solve for D we divide both sides by 50.
Simplifying 50 divided by 50 is one.
One times D is D, we have D equals
16,500 divided by 50 equals 330.
And remember, D is the number of day passes sold
and D plus 37 is the number of tournament passes sold.
So we know D equals 330 and D plus 37 is equal to 330
plus 37, which equals 367.
Before we write the answer as a complete sentence,
let's check this answer by using
these values in the equation here.
Where we substitute 330 for D and 467 for D plus 37,
which gives us 20 times 330, plus 30 times D plus 37 is 367.
And this must equal 17,610.
20 times 330 is 6,600, plus 30 times 367 is 11,010.
6,600 plus 11,010 is 17,610.
So because we have a true statement here,
this verifies our answer is correct.
So as a complete sentence,
330 day passes were sold.
367 tournament passes were sold.
Or I should say two complete sentences.
I hope you found this helpful.