Categories
Algebra Smart Math

[Smart Math] Algebra Problem 8

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

Algebra

Problem

A sum of $45 is made of 100 coins, partly of 50 cents and 25 cents. What is the number of 50 cents coins?

  1. 20
  2. 40
  3. 50
  4. 75
  5. 80

The Usual Method

[contentblock id=google-adsense-post]

Let the number of 50 cents coins be ‘x’, so the number of 25 cents coins will be (100 – x).
Thus, 0.5x+0.25(100-x)=45

\therefore 0.5x+25-0.25x=45

\therefore 0.25x=20

\therefore x=\frac{20}{0.25}=\frac{20\times 100}{25}=80

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

[contentblock id=google-adsense-post]

Use the alligation technique here. The average value of coin = \frac{45}{100}=0.45 or 45 cents
Thus,

Thus for every one 25 cents coins, there are four 50 cents coins. Dividing 100 coins in this ratio, we get 80 coins of 50 cents.

(Ans: 5)

Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published. Required fields are marked *