person(1) sells magazine subscriptions and earns
$P for every new subscriber
he signs up. person(1) also earns a
$Q weekly bonus regardless of how many
magazine subscriptions he sells.
person(1) sells magazine subscriptions and earns
$P for every new subscriber
she signs up. person(1) also earns a
$Q weekly bonus regardless of how many
magazine subscriptions she sells.
If person(1) wants to earn at least
$R this week, what is the minimum
number of subscriptions he needs to sell?
If person(1) wants to earn at least
$R this week, what is the minimum
number of subscriptions she needs to sell?
To solve this, let's set up an expression to show how much money person(1) will make.
Amount earned this week =
\qquadSubscriptions sold
\times Price per subscription
+ Weekly bonus
Since person(1) wants to make
at least $R this
week, we can turn this into an inequality.
Amount earned this week
\geq $R
Subscriptions sold \times Price per
subscription + Weekly bonus
\geq $R
We are solving for the number of subscriptions sold, so let
subscriptions sold be represented by the variable
x.
We can now plug in:
x \cdot $P + $Q \geq
$R
x \cdot $P \geq
$R - $Q
x \cdot $P \geq $R - Q
x \geq \dfrac{R - Q}{P}
\approx localeToFixed((R - Q) / P, 2)
Since person(1) cannot sell parts of
subscriptions, we round
localeToFixed((R - Q) / P, 2) up to
X.
x \geq \dfrac{R - Q}{P} =
(R - Q) / P
person(1) must sell at least X subscriptions this week.
For every level person(1) completes in
his favorite game, he earns
P points. person(1) already
has Q points in the game and wants to
end up with at least R points before
he goes to bed.
For every level person(1) completes in
her favorite game, she earns
P points. person(1) already
has Q points in the game and wants to
end up with at least R points before
she goes to bed.
Assuming person(1) can only get points by completing levels, what is the minimum number of levels that he needs to complete to reach his goal?
Assuming person(1) can only get points by completing levels, what is the minimum number of levels that she needs to complete to reach her goal?
To solve this, let's set up an expression to show how many points person(1) will have after each level.
Number of points =
\qquadLevels completed
\times Points per level +
Starting points
Since person(1) wants to have
at least R points
before going to bed, we can set up an inequality.
Number of points \geq R
Levels completed \times Points per level
+ Starting points \geq
R
We are solving for the number of levels to be completed, so
let the number of levels be represented by the variable
x.
We can now plug in:
x \cdot P + Q \geq
R
x \cdot P \geq R - Q
x \cdot P \geq R - Q
x \geq \dfrac{R - Q}{P}
\approx localeToFixed((R - Q) / P, 2)
Since person(1) won't get points unless
he completes the entire level, we round
localeToFixed((R - Q) / P, 2) up to
X.
Since person(1) won't get points unless
she completes the entire level, we round
localeToFixed((R - Q) / P, 2) up to
X.
x \geq \dfrac{R - Q}{P} =
(R - Q) / P
person(1) must complete at least X levels.
To move up to the maestro level in his piano
school, person(1) needs to master at least
R songs. person(1) has
already mastered Q songs.
To move up to the maestro level in her piano
school, person(1) needs to master at least
R songs. person(1) has
already mastered Q songs.
If person(1) can master
P songs per month, what is the minimum
number of months it will take him(1) to move to the
maestro level?
To solve this, let's set up an expression to show how many songs person(1) will have mastered after each month.
Number of songs mastered =
\quadMonths at school
\times Songs mastered per month
+ Songs already mastered
Since person(1) Needs to have
at least R songs
mastered to move to maestro level, we can set up an
inequality to find the number of months needed.
Number of songs mastered \geq
R
Months at school \times Songs mastered
per month
\qquad+ Songs already mastered
\geq R
We are solving for the months spent at school, so let the
number of months be represented by the variable
x.
We can now plug in:
x \cdot P + Q \geq
R
x \cdot P \geq R - Q
x \cdot P \geq R - Q
x \geq \dfrac{R - Q}{P}
\approx localeToFixed((R - Q) / P, 2)
Since we only care about whole months that
person(1) has spent working, we round
localeToFixed((R - Q) / P, 2) up to
X.
x \geq \dfrac{R - Q}{P} =
(R - Q) / P
person(1) must work for at least X months.