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= 2.4-------1
5w+x= 5.1---------2
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= 1.4--------1
7y+z= 2----------2
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=2.15--------1
3w+4x=2.05--------2
Multiplying equation 1 by 3 and equation 4 by 4
12w+9x=6.45--------3
12w+16x=8.2--------2
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) =2.15--------1
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= 4.2--------1
3y+ 7z= 5.95------2
Multiplying equation 1 by 3 and equation 2 by 2
6y+ 15z= 12.6-------3
6y+ 14z= 11.9--------4
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) = 4.2--------1
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
