Mathematics HL/SL/Studies Help

[Ezak]

As a rule of thumb, when working with inequalities, you can always square it if there are absolute values on both side of it, or absolute value on one side and an expression with an even exponent on the other.

[The Rainbow Connection]

Hey there, I need help with part d (i) and (ii) for this question. I've come across it before and get really stuck as I don't know how to sketch the graph. I have included the first part of the question & the answer for convenience. Thanks!

Mal is shopping for a school trip. He buys 50 tins of beans and 20 packets of

cereal. The total cost is 260 Australian dollars (AUD).

(a) Write down an equation showing this information, taking b to be the cost

of one tin of beans and c to be the cost of one packet of cereal in AUD. [1 mark]

ANS: 50b + 20c = $260

Stephen thinks that Mal has not bought enough so he buys 12 more tins of beans

and 6 more packets of cereal. He pays 66 AUD. (b) Write down another equation to represent this information. [1 mark]

ANS: 12b + 6c = $66

© Find the cost of one tin of beans. [2 marks]

ANS: $4

(d) (i) Sketch the graphs of these two equations.

(ii) Write down the coordinates of the point of intersection of the

two graphs. [4 marks]

The graph (if the attachment doesn't work) has pockets of cereal on the y-axis and tins of beans on the x-axis.

The y-intercept of the first line cuts at 13 and the x-axis at around 5.2; the second line cuts the y-axis at 11 and the x-axis at 5.5

I don't know how these values were found?

(the intersection is 4,3)

Edited November 9, 2013 by The Rainbow Connection

[bluedino]

Think of b and c as the normal x and y of a graph. (So as you can see the x axis is now like the b-axis and the y axis is now like the c-axis).

So graphing 12b + 6c = 66 is just like how you would graph 12x + 6y = 66. You might find it easier to graph if you make b/y the subject.

So then you'd have 6c = 66 - 12b.

--> c = 11 - 2b (This is the same as if you were graphing y = 11 - 2x).

So to find the y-intercept/where it cuts the y-axis (aka the c axis) it's b = 0, so c = 11.

To find the x-intercept/where it cuts the x-axis (aka the b axis) it's c = 0, so b = 5.5

(and to actually graph it, you just plot those 2 points, and by its mx+b form you know it's a straight line)

To graph 50b + 20c = 260 you'd go through the same process.

I hope this makes sense? I can try to clarify if something still doesn't make sense

Edited November 9, 2013 by bluedino

[The Rainbow Connection]

Think of b and c as the normal x and y of a graph. (So as you can see the x axis is now like the b-axis and the y axis is now like the c-axis).

So graphing 12b + 6c = 66 is just like how you would graph 12x + 6y = 66. You might find it easier to graph if you make b/y the subject.

So then you'd have 6c = 66 - 12b.

--> c = 11 - 2b (This is the same as if you were graphing y = 11 - 2x).

So to find the y-intercept/where it cuts the y-axis (aka the c axis) it's b = 0, so c = 11.

To find the x-intercept/where it cuts the x-axis (aka the b axis) it's c = 0, so b = 5.5

(and to actually graph it, you just plot those 2 points, and by its mx+b form you know it's a straight line)

To graph 50b + 20c = 260 you'd go through the same process.

I hope this makes sense? I can try to clarify if something still doesn't make sense

Brilliant - then put equations on GDC and ta-da! Thank you very much