# Khan/khan-exercises

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 Linear equation word problems
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 more than $R this week, what is the minimum number of subscriptions he(1) needs to sell? X subscriptions To solve this, let's set up an expression to show how much money person(1) will make. Amount earned this week = \qquadSubscriptions sold \times Price per subscription + Weekly bonus Since person(1) wants to make more than$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 more than 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

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.

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