Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?

The number is 6.25.

We will set up an equation for this.  Let x be the unknown number.  Subtracting 1.05 from it gives us

(x-1.05)

Multiplying the difference by 0.8 would give us

0.8(x-1.05)

Adding 2.84 to the product would give us

0.8(x-1.05)+2.84

Dividing the sum by 0.01 would give us

[0.8(x-1.05)+2.84]/0.01 = 700

We will start working backward, cancelling the division by 0.01 first by multiplying:

([0.8(x-1.05)+2.84]/0.01)*0.01 = 700*0.01

0.8(x-1.05)+2.84 =7

Subtract 2.84 from both sides:
0.8(x-1.05)+2.84-2.84 = 7-2.84
0.8(x-1.05) = 4.16

Use the distributive property on the left side:
0.8*x - 0.8*1.05 = 4.16
0.8x - 0.84 = 4.16

Add 0.84 to both sides:
0.8x - 0.84+0.84 = 4.16+0.84
0.8x = 5

Divide both sides by 0.8:
0.8x/0.8 = 5/0.8
x = 6.25