Question

Three ruler and two pencils cost £3.10

Two rulers and five pencils cost £3.90
Work out the cost of a ruler and pencil

Answer 1

To determine the cost of a single ruler and pencil, we use system of equations. After setting up and solving the equations using the elimination method, we find that the cost of one ruler is £0.70, and the cost of one pencil is £0.50.

Step-by-step explanation:

The student's question involves solving a system of linear equations to determine the cost of a single ruler and a single pencil. To solve this, we set up two equations based on the given information:

1. 3r + 2p = £3.10 (Three rulers and two pencils cost £3.10)
2. 2r + 5p = £3.90 (Two rulers and five pencils cost £3.90)

Where r represents the cost of one ruler and p represents the cost of one pencil.

We can solve these equations using substitution or elimination methods. For this example, let's use the elimination method:

1. Multiply the first equation by 2, and the second equation by 3, to make the coefficients of r the same:

• (2)×(3r + 2p) = (2)×£3.10 ⇒ 6r + 4p = £6.20
• (3)×(2r + 5p) = (3)×£3.90 ⇒ 6r + 15p = £11.70

Subtract the first new equation from the second:

• (6r + 15p) - (6r + 4p) = £11.70 - £6.20 ⇒ 11p = £5.50

Divide by 11 to find the price of one pencil:

• p = £5.50 / 11 ⇒ p = £0.50

Substitute the value of p into one of the original equations to find r:

• 3r + 2(£0.50) = £3.10 ⇒ 3r + £1.00 = £3.10
• 3r = £3.10 - £1.00 ⇒ 3r = £2.10
• r = £2.10 / 3 ⇒ r = £0.70

The cost of one ruler is £0.70, and the cost of one pencil is £0.50.

Answer 2

To find the cost of a ruler and the cost of a pencil, we can set up a system of equations using the given information. Let R be the cost of a ruler and P be the cost of a pencil.We know that 3R + 2P = 3.10 and 2R + 5P = 3.90Subtracting the first equation from the second, we get:5P - 3P = 3.90 - 3.10

2P = 0.80Dividing both sides by 2, we get:P = 0.40Substituting this value back into one of the original equations, we get:3R + 2(0.40) = 3.10

3R = 2.70

R = 0.90Therefore, the cost of a ruler is £0.90 and the cost of a pencil is £0.40.

Step-by-step explanation: