Paul has £7.80 pocket money each week.
He always saves 1/3 of it.
With the remaining money he spends on
comics and the rest on sweets.
(i) How much does he save?
(ii) How much is spent on comics?
(iii) How much does he spend on sweets?

i) $2.60 is money he saves each week

ii( iii)  $5.20 to spend on comics and sweets.

You need more info to determine how he spends his money thereafter.

Lets say x = sweets and y = comics.

and lets say he spends under 1/3 on sweets

2(1 1/5x + 1 1/2y) = xy

2 2/5x + 3y = xy

xy = 5 2/5

Step-by-step explanation:

i) 7.80 /3 = 2.60  = $2.60

ii) 7.80-2.6 = 5.20 = $5.20

iii) algebra example or refer to question for more info not shown.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.