Delaney has $830 worth
of $10 and $14 stock shares.
The number of $14 shares is five more
than twice the number of $10 shares.
How many shares of each stock does she have?
To begin, we need to add expressions
for the number of $10 shares
and the number of $14 shares.
And since we're told the number of $14 shares
is five more than twice the number of $10 shares,
let's first let x equal the number of $10 shares.
And now from here, again, because the number of $14 shares
is five more than twice the number of $10 shares,
we can use the expression
two x plus five for the number of $14 shares.
Notice twice the number of $10 shares
would be two times x, or two x,
and we want five more than twice the number of $10 shares,
which is why the expression for the number of $14 shares
is two x plus five.
We also know the total value is $830,
so now we can write a value equation
that we can then solve to answer the question.
The value equation is going to be
the value of the first stock
times the number of shares of the first stock
plus the value of the second stock
times the number of shares of the second stock
must equal the total value.
So the value of the first stock is $10 per share,
and we have x shares of the $10 shares.
And therefore the total value of the $10 shares
is $10 times x.
Leaving the units of dollars off,
that gives us 10 times x.
And then we have plus the total value
of the $14 shares is going to be $14
times the number of shares,
which is $14 times the quantity two x plus five,
which gives us for our equation
14 times the quantity two x plus five
must equal the total value of $830.
And now we need to solve the equation for x.
On the left, 10 times x is equal to 10x.
And then we distribute 14 here.
14 times two x gives us plus 28x.
And then 14 times five is equal to 70,
giving us plus 70 equals 830.
Combining like terms on the left,
10x plus 28x is 38x,
giving us 38x plus 70 equals 830.
Next step is to add or subtract to isolate 38x.
And therefore we subtract 70 on both sides.
Simplifying, we have 38x
is equal to 830 minus 70,
which is equal to 760.
The last step is to divide both sides by 38
in order to solve for x.
Simplifying, 38 divided by itself simplifies to one.
One times x is x.
We have x equals 760 divided by 38
which is equal to 20.
Now that we know x is equal to 20,
we can determine how many shares
of each stock Delaney has.
And let's do this on the next slide.
Again, we just found x is equal to 20,
so we know Delaney has 20 $10 shares.
The number of $14 shares is equal
to two x plus five.
Substituting 20 for x,
we have two times 20 plus five
which is equal to 40 plus five
which is equal to 45.
We now know Delaney has 20 $10 shares
and 45 $14 shares.
Before we go, let's verify our solution
by verifying the value equation below,
which is $10 times 20 shares
plus $14 times 45 shares
is equal to $830.
Going to the calculator,
you can see our equation is true,
verifying our solution is correct.
I hope you found this helpful.