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?
Accepted Solution
A:
The number is 6.25.
We will set up an equation for this.Β Let x be the unknown number.Β 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