Lydia's school is holding a candy fundraiser. They are selling lollipops for $0.50 and candy bars for $1.50 Lydia buys 6 lollipo
1 answer:
Answer:
8
Step-by-step explanation:
Let's say that the amount of lollipops Lydia buys is represented by x and the number of candy bars is represented by y. For each x, Lydia spends 0.50, and for each y, Lydia spends 1.50. This means that the total amount she spends can be represented by the equation 0.50*x+1.50*y. Our equation is then 0.50*x+1.50*y=15
Using our equation, we can plug 6 in for x, resulting in 0.50*6+1.50*y=15, so
In this set of equations, we plugged 6 in, multiplied it out, then subtracted 3 from both sides, and finally divided both sides by 1.50 to get 8 as our answer.
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The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for 
which indeed gives the recurrence you found,
but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that
, and substituting this into the recurrence, you find that 
for all 
.
Next, the linear term tells you that
, or 
.
Now, if
is the first term in the sequence, then by the recurrence you have
and so on, such that
for all 
.
Finally, the quadratic term gives
, or 
. Then by the recurrence,
and so on, such that
for all.
Now, the solution was proposed to be
so the general solution would be
which indeed gives the recurrence you found,
but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that
Next, the linear term tells you that
Now, if
and so on, such that
Finally, the quadratic term gives
and so on, such that
for all
Now, the solution was proposed to be
so the general solution would be