randRange(20, 40) randRange(2, 10) randRange(30, 100) ceil((R - Q) / P) randRange(1,3)

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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.

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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?

subscriptions
[ $("#guessans").val(), $("#firsttext").val(), $("#secondtext").val() ]
var correct = X; var solutionDiv = $("<div>").text(correct); var validator = Khan.answerTypes.number.createValidator(solutionDiv); return validator(guess[0]);
if (guess != null) { $("#guessans").val(guess[0]); } else { $("#guessans").val(""); if ($("#firsttext").length > 0) { $("#firsttext").text(""); $("#secondtext").text(""); } }
if (guess != null && $("#firsttext").length > 0) { guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]); guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]); }
an integer, like 6

To solve this, let's set up an expression to show how much money person(1) will make.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.

10 * randRange(100 / 10, 500 / 10) 10 * randRange(300 / 10, 1000 / 10) 10 * randRange(2000 / 10, 4000 / 10) ceil((R - Q) / P) randRange(1,3)

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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.

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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.

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

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

levels
[ $("#guessans").val(), $("#firsttext").val(), $("#secondtext").val() ]
var correct = X; var solutionDiv = $("<div>").text(correct); var validator = Khan.answerTypes.number.createValidator(solutionDiv); return validator(guess[0]);
if (guess != null) { $("#guessans").val(guess[0]); } else { $("#guessans").val(""); if ($("#firsttext").length > 0) { $("#firsttext").text(""); $("#secondtext").text(""); } }
if (guess != null && $("#firsttext").length > 0) { guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]); guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]); }
an integer, like 6

To solve this, let's set up an expression to show how many points person(1) will have after each level.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.

randRange(5, 50) randRange(50, 200) randRange(1, 10) ceil(( R - Q ) / P) randRange(1,3)

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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.

[Click to learn about the “ What? Why? How?" strategy]

To use this strategy, ask yourself these “ What? Why? How?" questions after each hint in a problem.
What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?
As a reminder to ask yourself these questions, they will sometimes appear in purple.

What if I can’t do it?

Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.

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

months
[ $("#guessans").val(), $("#firsttext").val(), $("#secondtext").val() ]
var correct = X; var solutionDiv = $("<div>").text(correct); var validator = Khan.answerTypes.number.createValidator(solutionDiv); return validator(guess[0]);
if (guess != null) { $("#guessans").val(guess[0]); } else { $("#guessans").val(""); if ($("#firsttext").length > 0) { $("#firsttext").text(""); $("#secondtext").text(""); } }
if (guess != null && $("#firsttext").length > 0) { guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]); guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]); }
an integer, like 6

To solve this, let's set up an expression to show how many songs person(1) will have mastered after each month.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.

What does this step mean to you?
Why is it helpful to take this step?
How do you know this step is right?

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.