randRange(20, 40) randRange(2, 10) randRange(30, 100) ceil((R - Q) / P)

person(1) sells magazine subscriptions and earns $P for every new subscriber he(1) signs up. person(1) also earns a $Q weekly bonus regardless of how many magazine subscriptions he(1) sells.

If person(1) wants to earn at least $R this week, what is the minimum number of subscriptions he(1) needs to sell?

X subscriptions

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 ((R - Q) / P).toFixed(2)

Since person(1) cannot sell parts of subscriptions, we round ((R - Q) / P).toFixed(2) up to X.

x \geq \dfrac{R - Q}{P} = (R - Q) / P

person(1) must sell at least X subscriptions this week.

10 * randRange(100 / 10, 500 / 10) 10 * randRange(300 / 10, 1000 / 10) 10 * randRange(2000 / 10, 4000 / 10) ceil((R - Q) / P)

For every level person(1) completes in his(1) favorite game, he(1) earns P points. person(1) already has Q points in the game and wants to end up with at least R points before he(1) goes to bed.

What is the minimum number of complete levels that person(1) needs to complete to reach his(1) goal?

X levels

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 ((R - Q) / P).toFixed(2)

Since person(1) won't get points unless he(1) completes the entire level, we round ((R - Q) / P).toFixed(2) up to X.

x \geq \dfrac{R - Q}{P} = (R - Q) / P

person(1) must complete at least X levels.

randRange(5, 50) randRange(50, 200) randRange(1, 10) ceil(( R - Q ) / P)

To move up to the maestro level in his(1) piano school, person(1) needs to master at least R songs. person(1) has already mastered Q songs.

If person(1) can typically master P songs per month, what is the minimum number of months it will take him(1) to move to the maestro level?

X months

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 ((R - Q) / P).toFixed(2)

Since we conly care about whole months that person(1) has spent working, we round ((R - Q) / P).toFixed(2) up to X.

x \geq \dfrac{R - Q}{P} = (R - Q) / P

person(1) must work for at least X months.