Question

After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight (in pounds)?

Answer 1

Answer:

175 pounds

Step-by-step explanation:

21×100÷12

Answer 2

Answer:

Step-by-step explanation:

From the problem we know that 12% of Lisa's original weight is 21 pounds. Let's call Lisa's original weight x and rewrite what we know from the question in terms of x.

We can convert 12% into a decimal - 0.12. We can also recognize that the word "of" used in a word problem often means you need to multiply. So, we can multiply 0.12 by x because we know 12% of Lisa's original weight.

0.12x = 21

To solve this equation, we need to isolate x, so we can divide both sides by 0.12.

x = 175. ==> Lisa's original weight was 175 pounds.

If you don't have a calculator or would like to learn another way to solve this problem, you can use proportions.

We know that 12% of x is 12, so what is 100% of x? (this is another way to rewrite the question)

We can contine to rewrite this by writing

$\frac{12}{21} = \frac{100}{x}$

We can write this because we know that the ration of 12% to 21 pounds is going to be the same ratio of 100% to Lisa's entire body weight.

We can multiple by both sides of the equation by  $\frac{21x}{21x}$, which is equal to 1 so it won't change the value of the equation, to remove the denominators. Then, we'll end up with:

12x = 100*21

12x = 2100

x = 175