Question

Four rulers and three pencils cost £2.15 Three rulers and four pencils cost £2.05 Work out the cost lf a ruler and the cost of a pencil

Answer 1

The cost of a ruler is £0.35 and the cost of a pencil is £0.25.

Step-by-step explanation:

Let's solve this problem using a system of equations approach:

Let's assume that the cost of a ruler is x and the cost of a pencil is y.

According to the first statement, 4 rulers and 3 pencils cost £2.15, so we can write the equation: 4x + 3y = 2.15.

According to the second statement, 3 rulers and 4 pencils cost £2.05, so we can write the equation: 3x + 4y = 2.05.

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of elimination:

Multiply the first equation by 3 and the second equation by 4 to make the coefficients of x in both equations the same:

12x + 9y = 6.45

12x + 16y = 8.2

Subtract the first equation from the second equation to eliminate x:

12x + 16y - (12x + 9y) = 8.2 - 6.45

7y = 1.75

Divide both sides of the equation by 7:

y = 0.25

Now substitute the value of y back into one of the original equations (let's use the first equation):

4x + 3(0.25) = 2.15

4x + 0.75 = 2.15

Subtract 0.75 from both sides of the equation:

4x = 1.4

Divide both sides of the equation by 4:

x = 0.35

Therefore, the cost of a ruler is £0.35 and the cost of a pencil is £0.25.

Answer 2

The cost of 1 ruler and 1 pencil are $0.35 and $0.25 respectively,

Step-by-step explanation:

Let the cost of 1 ruler be x

Let the cost of 1 pencil be y

Cost of 4 rulers = 4x

Cost of 3 rulers = 3x

Cost of 3 pencils = 3y

Cost of 4 pencils = 4y

We are given that Four rulers and three pencils cost £2.15

4x+3y=2.15 ---- Black line

We are also given that Three rulers and four pencils cost £2.05

3x+4y=2.05 --- Red line

Plot the lines on the graph

Point of Intersection of lines is (0.35,0.25)

Cost of a ruler = $0.35

Cost of a pencil = $0.25

Hence The cost of 1 ruler and 1 pencil are $0.35 and $0.25 respectively,