Video: Solving Word Problems Involving Percentages

A butcher reported that his sales figures for the current year were 87% of last year’s figures. Given that he sold 2990 kg of produce this year, determine how many kilograms he sold last year, giving your answer to the nearest kilogram.

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Video Transcript

A butcher reported that his sales figures for the current year were 87 percent of last year’s figures. Given that he sold 2990 kilograms of produce this year, determine how many kilograms he sold last year, giving your answer to the nearest kilogram.

We’re told that, this year, the butcher sold 87 percent of last year’s figures. Therefore, we can say that this year is equal to 87 percent. And last year is equal to 100 percent. This year, the butcher has sold 2990 kilograms. Therefore, 87 percent, this year’s percentage, is equal to 2990.

One way of solving this problem will be by scaling up and down. We know 87 percent of the quantity. And we want to calculate 100 percent. As 87 percent is equal to 2990, we can work out one percent by dividing both sides of the equation by 87. 87 divided by 87 is equal to one. 2990 divided by 87 is equal to 34.3678 and so on. It is important at this point to not round your answer. This will ensure that our final answer is as accurate as possible.

We want to work out 100 percent. This means that we need to multiply both sides of this equation by 100. One multiplied by 100 equals 100. 34.3678 multiplied by 100 is equal to 3436.78 and so on. We were asked to round this to the nearest kilogram. So the deciding number is the first number after the decimal point. This number is seven. As seven is greater than five, we will round up, giving us an answer of 3437 kilograms. This means that the butcher produced 3437 kilograms of produce last year.

A quick check at this stage would be to calculate 87 percent of 3437. If our answer is 2990, then we know we were correct. 87 percent is the same as 0.87. And the word “of” in maths means times. We can therefore multiply 0.87 by 3437. This is equal to 2990 kilograms to the nearest kilogram. We can therefore say that 87 percent of 3437 is equal to 2990. So the butcher’s sales figures are 87 percent of last year’s figures.

Finally, we will just show you a quick method that we could use using the initial numbers, 2990 kilograms and 87 percent. To work out the original or old value, we can divide our new value by the decimal equivalent of the percentage, in this case, 2990 divided by 0.87. This will give us the answer of 3437 kilograms in one step.

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