Sorry if this is long <3

1) Two rulers and one pencil cost £2.40
Five rulers and one pencil cost £5.10
Work out the cost of a ruler and the cost of a pencil.

2) Four apples and one banana cost £1.40
Seven apples and one banana cost £2.00
Work out the cost of an apple and the cost of a banana.

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

4) Two apples and five bananas cost £4.20
Three apples and seven bananas cost £5.95
Work out the cost of an apple and the cost of a banana.

Step-by-step explanation:

Dear friend you don't have to be sorry for the length of the question , for now let's fix the problem.

Since the two items are rulers, pencils, apples and bananas

Let ruler be w

Pencil be x

Apple be y

Banana be z

Since the word problem seeks to identify two unknowns we will be solving all word problems simultaneously

1. 2w+5x= 2.41

5w+x= 5.12

Multiplying equation 2 by 5 and Subtracting to eliminate x

2w+5x=2.4

- 10w+5x=10.2

=-8w+0=-7.8

w=7.8/8

w= £0.975

Substituting w in equation 1 to find x we have

2(0.975) +5x= 2.4

1.95+5x= 2.4

5x=2.4-1.95

5x= 0.45

x=0.45/5

x= £0.09

The cost of one ruler is £0.975

And one pencil is £0.09

2. 4y+z= 1.41

7y+z= 22

Subtracting to eliminate z we have

-3y+0=-0.6

3y=0.6

y=0.6/3

y= 0.2

Substituting y = 0.2 in equation 1 to find z

4(0.2)+z= 1.4

0.8+z= 1.4

z= 1.4-0.8

z= 0.6

An apple is £0.2 and

a banana is £0.6

3. 4w+3x=2.151

3w+4x=2.052

Multiplying equation 1 by 3 and equation 4 by 4

12w+9x=6.453

12w+16x=8.22

Subtracting equation 2 from 3

0w-7x= -1.75

7x= 1.75

x= 1.75/7

x= 0.25

Substituting x = 0.25 in equation 1 to find w

4w+3(0.25) =2.151

4w+ 0.75= 2.15

4w= 2.15-0.75

4w= 1.4

w= 1.4/4

w= 0.35

A ruler cost £0.35

A pencil cost £0.25

4. 2y+ 5z= 4.21

3y+ 7z= 5.952

Multiplying equation 1 by 3 and equation 2 by 2

6y+ 15z= 12.63

6y+ 14z= 11.94

Subtracting equation 4 from equation 3 we have

0y+ z =0.7

z= 0.7

Substituting z= 0.7 in equation 1 to find y

2y+ 5(0.7) = 4.21

2y+3.5= 4.2

2y=4.2-3.5

2y=0.7

y= 0.7/2

y= 0.35

An apple cost £0.35

A banana cost £0.7

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.