A) x and y are two numbers taken from the list below. 5,6,7,8,9,10

(i) What values of x and y will make 3x - 2y equal zero? x=? Y=?

(ii) Work out the greatest possible value of 3x - 2y.

(iii) Work out the least possible value of 3x - 2y.

b) Find the value of
5(a - 4b) when a = -7 and b= 1/4

a)

i) we have the equation:

3*x - 2*y

We want to find a common multiple of 3 and 2.

One can be:

3*6 = 18

2*9 = 18

And both numbers 6 and 9 are on the list, then if we take:

x = 6, y = 9

we get:

3*6 - 2*9 = 18 - 18 = 0

The solution is x = 6, y = 9.

ii) The greatest possible value of:

3*x - 2*y

Will be when x is the largest value of the list (because it is on the positive term) and y is the smallest value on the list (because it is on the negative term)

then we need to have x = 10, y = 5

The value will be:

3*10 - 2*5 = 30 - 10 = 20

iii) Now we want to have the smallest value on x, and the largest one on y, then:

x = 5, y = 10

The smallest value of the equation will be:

3*5 - 2*10 = 15 - 20 = -5

B) We want to solve:

5*(a - 4*b)

when:

a = -7

b = 1/4

This is kinda easy, we just need to replace the variables in the equation to get:

5*(a - 4*b) = 5*(-7 - 4*(1/4)) = 5*(-7 - 4/4) = 5*-8 = -40