Alex buys 2 rulers and 2 rubbers for £3.Alex buys 3 rulers and 4 rubbers for £5.75.Work out the cost of one ruler and one rubber.

To solve this problem, we can use a system of linear equations.

Let's denote: R = cost of one ruler E = cost of one eraser (rubber)

From the problem, we have the following two equations:

2R + 2E = 3 (equation 1) 3R + 4E = 5.75 (equation 2)

We can simplify equation 1 by dividing by 2, which gives us:

R + E = 1.5

Now we have a simpler system of equations:

R + E = 1.5 (equation 3) 3R + 4E = 5.75 (equation 4)

We can multiply equation 3 by 3 to make the R terms in both equations equal:

3R + 3E = 4.5 (equation 5)

Now we have:

3R + 3E = 4.5 (equation 5) 3R + 4E = 5.75 (equation 4)

We can subtract equation 5 from equation 4 to find the value of E:

E = 5.75 - 4.5 = 1.25

Substitute E = 1.25 into equation 3 to find the value of R:

R = 1.5 - 1.25 = 0.25

So, one ruler costs £0.25 and one eraser costs £1.25.