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Algebra Smart Math

[Smart Math] Algebra Problem 24

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

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

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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

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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.

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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