Math Help - Algebra problem

1. Algebra problem

I am completely stuck on this, please explain clearly.

Many thanks

In this question x * y means (x+2y)/3 if x < y, and (2x + y)/3 if x is larger or equal to y.

a) Find the value of

i) 5 * 8
ii) 8 * 5

b) Solve

iii) x * 7 = 8
iv) x * (x-1) = 4 2/3 (that's 4 followed by 2/3 as a fraction)

c) In terms of p and q, find the possible values of (p * q) *p, explaining carefully how you choose which calculations to make.

2. In this question x * y means $\frac{x+2y}{3}$ if x < y, and $\frac {2x+y}{3}$ if x is larger or equal to y.

a) Find the value of

i) 5 * 8

So x = 5 and y = 8. Clearly, x<y, so just substitute the values 'x=5' and 'y=8' into the first equation to give:

$\frac{5+(2)(8)}{3}$

This simplifies to give an answer of 7.

Can you apply this to part ii)?

Then for part b) iii)
We know that y=7 and the answer is 8. Substituting that into the original equation:
$\frac{x+2y}{3}$

Gives:

$\frac{x+2(7)}{3}=8$
$\frac{x+14}{3}=8$
$x+14=24$
$x=10$

As this value of x is greater than our value of y, however, this is incorrect as we can only use this equation 'if x < y'

So you'll have to substitute the values into the second equation.

$\frac {2x+(7)}{3}=8$
$2x+7=24$
$2x=17$
$x=\frac{17}{2}=8.5$

Can you apply this to part ii?

FInally, part c. I don't understand part c as it seems to me that there could be almost infinite values for that equation. Is it not just trial and error?

3. Originally Posted by Natasha1
I am completely stuck on this, please explain clearly.

Many thanks

In this question x * y means (x+2y)/3 if x < y, and (2x + y)/3 if x is larger or equal to y.

c) In terms of p and q, find the possible values of (p * q) *p, explaining carefully how you choose which calculations to make.
I think there are two possibilities:

1. P<q and (P * q)>p
2. p>q and (p * q)<p

1. $[p * q] * p = [(p+2q)/3]* p$ {In this case I have used ,(x+2y)/3 if x < y, by letting p=x and q=y}
$= [2([(p+2q)/3])+p]/3$. { In this case I have used, (2x + y)/3 if x is larger or equal to y, by substituting p=y and [(p+2q)/3] = x}
you can try the second part!!