Help wıth question

[PolySquared]

Hi guys,

Can someone please solve this question and explain the reason behind the solution. Specifically, could you explain how and the reasons behind the way you set up the equation. Thanks.

Tickets for a concert are available at two prices. The more expensive ticket is $30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for $1800.

[jazzycab]

Hi guys,

Can someone please solve this question and explain the reason behind the solution. Specifically, could you explain how and the reasons behind the way you set up the equation. Thanks.

Tickets for a concert are available at two prices. The more expensive ticket is $30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for $1800.

To do any problem of this type, you should identify what you are being asked for from the outset (and therefore define the necessary variables).
In this question, we're asked to find the cost of each type of ticket (cheaper and more expensive), so we might call these c and e respectively (in dollars).
From here, you need to identify each piece of mathematical information and relate it to these two variables:

This is from the fact that the more expensive tickets are $30 more than the cheap tickets.

The tricky part hereafter is that we don't know anything about the number of tickets sold, but let's say that in the statement regarding the $1800, there could be n expensive tickets sold (and therefore n+10 cheaper tickets could be sold):

This gives us a system of three simultaneous equations to solve. Substituting equation (1) into equation (2) gives:

Transposing equations (4) and (3) respectively, then using substitution gives:

[PolySquared]

To do any problem of this type, you should identify what you are being asked for from the outset (and therefore define the necessary variables).
In this question, we're asked to find the cost of each type of ticket (cheaper and more expensive), so we might call these c and e respectively (in dollars).
From here, you need to identify each piece of mathematical information and relate it to these two variables:

This is from the fact that the more expensive tickets are $30 more than the cheap tickets.

The tricky part hereafter is that we don't know anything about the number of tickets sold, but let's say that in the statement regarding the $1800, there could be n expensive tickets sold (and therefore n+10 cheaper tickets could be sold):

This gives us a system of three simultaneous equations to solve. Substituting equation (1) into equation (2) gives:

Transposing equations (4) and (3) respectively, then using substitution gives:

Thank you for your response, I really appreciate it.

[PolySquared]

To do any problem of this type, you should identify what you are being asked for from the outset (and therefore define the necessary variables).
In this question, we're asked to find the cost of each type of ticket (cheaper and more expensive), so we might call these c and e respectively (in dollars).
From here, you need to identify each piece of mathematical information and relate it to these two variables:

This is from the fact that the more expensive tickets are $30 more than the cheap tickets.

The tricky part hereafter is that we don't know anything about the number of tickets sold, but let's say that in the statement regarding the $1800, there could be n expensive tickets sold (and therefore n+10 cheaper tickets could be sold):

This gives us a system of three simultaneous equations to solve. Substituting equation (1) into equation (2) gives:

Transposing equations (4) and (3) respectively, then using substitution gives:

Are there any alternatives to solving this question that doesn’t involve simultaneous equations?

[jazzycab]

I suppose you could use a guess and check type technique, but that could potentially take a much longer time and may not get you full marks on a question of this type. From my experience with Methods, if you were to be assessed on this in an exam, it would most likely be on exam 2, so you'd be able to set up the equations, then skip the solving by having your CAS do that grunt work.

[Sine]

Why is the derivative of 2e is 0?
Steps and explanation please! Cheers

2e is a constant, this is because e = 2.71828 (to 5 decimal places)
So if we were to sketch 2e it would be a horizontal line at y = 2e which is y = 5.43656. As we know the derivitive is the rate of change of the function and we can input certain x values for that. In this case the gradient is constant (straight line) and zero (horizontal line)

[microwaverdetective]

If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B) without evaluating A or B.
Working please! Cheers

[The Special One]

You can solve this via matrices on the CAS if that's more your style.

My teacher always said it was a waste of time but I personally found it faster with a lower margin for error

EDIT

Ignore all that misread the question thought it was a simultaneous equation

[VanillaRice]

If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B) without evaluating A or B.
Working please! Cheers

Is this a Methods or Specialist question? It seems to be more of a specialist question, with particular use of the compound angle formula for tan.

[keltingmeith]

Is this a Methods or Specialist question? It seems to be more of a specialist question, with particular use of the compound angle formula for tan.

Could be an old edition of a textbook - they used to be in the methods study design, but you are right, they're definitely out now.

[JamesMaths]

Could I please put my solution to this question here?
Thanks,
James.