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VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: chuckjefster90 on April 18, 2010, 05:37:59 pm

Title: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 05:37:59 pm: Hey Guys, I'm unable to solve this problems. Would you be able to help me solve them? The answers are at the bottom, I just need to know how to get them. Thanks Heaps.

1. After spending 5/8 of his salary, Tom has $315 left. What is his salary?

2. 11,12,13 are consexutive integers. Find another 3 consecutive integers which add to 114.

3. A square and an equilateral triangle have the same perimeter. The sides of the triangle are 4cm longer than the sides of the square.
How long is one side of the square?

4. If Mrs Nguyen is 38 years old and her daughter is 8 years old, in how many years will Mrs Nguyen be 3 times as old as her daughter?

5. Tim runs between 2 places, A and B at 10km/hr and cucles back again at 20 km/hr. The total time taken to run and cucle is 3 hours. If the disance between A and B is x kim, form an equation in x and solve it to find the distance between A and B.

6. THe sum of the interior angles of a polygon with 'n' sides is (2n-4) right angles. If each interior angle is a regular polygon is 135 degrees, how many sides has the polygon?

7. The hypotenuse of a right angles triangle is (x + 5) cm in length and the other 2 sides are 5 cm and (x + 4) cm. Use the Theorem of Pythagoras to write an equation in x and solve it to find the lengths of the unknown sides of the triangle.

Answers:
1) $840 2) 37,38,39 3) 12 cm 4) 7 Years 5) 20 km 6) 8 (an octagon) 7) 12 and 13 cm
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: the.watchman on April 18, 2010, 05:40:05 pm: 1) $Salary = 315 \times \frac{8}{3} = 105 \times 8 = 840$

2) Let x be the middle number

$(x-1) + x + (x+1) = 114$

$3x = 114$

$x=38$

So the numbers are 37, 38 and 39

3) $4\times SideLengthOfSquare= 3\times SideLengthOfTriangle = 3\times (SideLengthOfSquare + 4)$

$SideLengthOfSquare = 12$

4) $38+n = 3(8+n)$

$2n = 14$

$n=7$

I'm going out now, someone wanna take over? :P
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: superflya on April 18, 2010, 05:42:24 pm: q2) n+n+1+n+2=114 3n+3 =114 n=37 so 37,38,39
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: m@tty on April 18, 2010, 06:06:24 pm: 5. $Time=\frac{Distance}{Speed}$ $T=\frac{D}{V}$

$T = \frac{x}{10} + \frac{x}{20}=3$

$20 \cdot 3= 2x+x$

$3x=60$

$x=20 \ km$

6. $\sum angles = (2n-4) \times 90^\circ$

Note that the number of sides is the number of angles.

$\therefore 135n=90(2n-4)$

$45n=360$

$n=8$

7. By Pythagoras for a right angled triangle $a^2+b^2=c^2$

So, $5^2+(x+4)^2=(x+5)^2$

$25+x^2+8x+16=x^2+10x+25$

$2x=16$

$x=8$

So lengths are 5cm, 12cm and 13cm.
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: |ll|lll| on April 18, 2010, 07:32:04 pm: 7. The hypotenuse of a right angles triangle is (x + 5) cm in length and the other 2 sides are 5 cm and (x + 4) cm. Use the Theorem of Pythagoras to write an equation in x and solve it to find the lengths of the unknown sides of the triangle.

(x+5)² = 5² + (x+4)²

x² + 10x + 25 = 25 + x² + 8x +16

2x = 16
x= 8

Sub x into the sides,
8+5 = 13 and 8+4 = 12
:)

Try to remember that 3, 4, 5 and 5, 12, 13 form right angle triangles.
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: |ll|lll| on April 18, 2010, 07:37:17 pm: Quote from: the.watchman on April 18, 2010, 05:40:05 pm
3) $4\times SideLengthOfSquare= 3\times SideLengthOfTriangle = 3\times (SideLengthOfSquare + 4)$

$SideLengthOfSquare = 12$
Hey watchman, is that some kind of formula? :D
I go about doing it this way:

let side length of square be x
4x = 3(x+4)
And then solve for x.

And oops, sorry, just found out that matty did qn 7 lol
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: the.watchman on April 18, 2010, 07:38:40 pm: Nope, it's exactly the same as what you did, except I couldn't be bothered defining a variable :P
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 08:12:17 pm: you guys are legends!
Thanks heaps!!! :)
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 08:49:11 pm: yeahh further haha
forgot all of it haha
hey can you like explain q3?
im still a bit confused on that
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 08:54:25 pm: wait no worries i got it now :)
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 08:58:44 pm: hey watchman, sorry third comment but for question four what is 'n' suppose to stand for?

thanksss
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: the.watchman on April 18, 2010, 09:05:46 pm: Quote from: cherylim23 on April 18, 2010, 09:02:10 pm
It stands for the no. of years

... after which the conditions set out by the question are met :P
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: chuckjefster90 on April 18, 2010, 09:28:29 pm: thankss this all helped me so mcuh :)
ill be asking you guys defs if i need help!

thanks again :D
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: the.watchman on April 18, 2010, 09:29:32 pm: Quote from: chuckjefster90 on April 18, 2010, 09:28:29 pm
thankss this all helped me so mcuh :)
ill be asking you guys defs if i need help!

thanks again :D

No probs, happy to help :)
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: crayolé on April 18, 2010, 09:32:28 pm: What further module is this?
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: Blakhitman on April 18, 2010, 09:42:00 pm: I wish I knew VN last year, you are one lucky person OP.

(think you're in year 11?)
Title: Re: Using Equations to Solve a Problem - Need Help to solve these without a calculat
Post by: the.watchman on April 18, 2010, 09:54:52 pm: Quote from: Blakhitman on April 18, 2010, 09:42:00 pm
I wish I knew VN last year

Lol, I'm glad I found this place for yr 11 :)