Sarah used to earn 80£ per week, however she was given a 5% pay rise, what are her weekly earnings now?

METHOD 1:Required Formula: Percentage Change(%)=100x(Final value -Initial value)/(Initial value) Percentage Change = 5% (this is positive 5% since Sarah has a price raise, if Sarah had a 5% wage decrease then use -5 instead for the percentage change value)The Final Value (her current weekly earnings) = unknownThe Initial Value (her weekly earnings before the pay rise) = 80£(1) 5 = 100 x (Final value -80)/80 The 100 in the formula is used for converting the percentage (5%) into it's decimal value = 0.05, (move the 100 to the other side: 5/100 = 0.05)(2) 0.05 = (Final value - 80)/80This time multiply both sides of the equation by 80 to eliminate the fraction (Final value - 80)/80 on the right-hand side of the equation(3) 0.05 x 80 = 80(Final value - 80)/80On the left hand side 0.05 x 80 = 4 (shown below), and on the right hand side the (Final value - 80) is multiplied by 80 and divided by 80 so these functions cancel out leaving below:(4) 4 = Final value – 80Now we know that Sarah is earning 4£ more per week. However finally to find out what she earns now, add 80 to both sides of the equation (to cancel out the -80 on the right hand side)(5) 4+80 = Final value - 80 + 80(6) 84 = Final value (her current weekly earnings)The percentage change formula will work for all types of percentage change questions however it is quite long and it's important to remember: A) Get the sign of the percentage change correct, ie whether it's a positive change or negative changeB) Remember that we take the difference as (Final value - Initial value), even if the Final value is less than the initial value, and divide by the Initial value always afterwards
METHOD 2: Get the actual increase in weekly earnings instead of just the percentage increase in weekly earnings:Find out 5% and convert to a decimal, that's 5/100 or 0.05 and then multiply by 80£. 80x0.05= 4£. (That shows that 4 is 5% of 80)Now we learn that she earns 4£ (5%) more. However, to find her total earnings now, you add 4£ to 80£ = 84£.
METHOD 3:To understand the "change factor".5% is 0.05 as a decimal, and here if you multiply 0.05 x 80 you get 4£ (that's the extra earnings that Sarah earns)In the same way:100% is 1 as a decimal, and here if you multiply 1 x 80 you get 80£ (that's the original amount that Sarah was earning)Here we want to find the final weekly earnings, that's what she was earning originally + the extra earningsMathematically that can be represented by: 100% (what she earns originally) + 5% (extra), (she now earns 105% what she used to earn)Or decimally that's 1 + 0.05 = 1.05 times what she used to earnSo in this case to find a 5% rise, multiply the original Wage by 1.05. 80x1.05=84 to find the total earnings after the raise a lot quicker. Inital value x change factor = Final valueThis is a quick method for calculating percentage change when you know the percentage change.For example, if Sarah had a 10% wage decrease This time, 10% is 0.1 as decimal however since it's a 10% wage decrease this is now negative, -0.1.1+-0.1 = 0.9 change factorInital value x change factor = Final value80 x 0.9 = 72£ which would be Sarah's wage after a 10% wage decrease