Categories

# [Smart Math] Algebra Problem 24

Here’s and example of a SMART MATH problem for ALGEBRA.

### Problem

If Mira was twice as heavy as she is, she would be 10 lbs lighter than her mother; if she were to lose 10 lbs, she would be 75% of her present weight. How much does Mira’s mother weigh?

1. 60 lbs
2. 70 lbs
3. 80 lbs
4. 90 lbs
5. 100 lbs

### The Usual Method

Let the weight of Mira be ‘x’ years and that of her mother be ‘y’ years.

Hence,

$2x+10=y$                                …… Eq. 1

and       $x-10=0.75x$                            …… Eq. 2

From Eq. 2,

$0.25x=10$

$\therefore x=40$

$\therefore y=2\times 40+10=$ 90 lbs

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

If 10 lbs is reduced from a weigh, than it becomes 75% of the original. Thus the reduction of 10 lbs is equivalent to 25%. Hence 100% is equal to 40 lbs. Thus Mira’s weight is 40 lbs and her mother’s weight is $2\times 40+10=$ 90 lbs.