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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 46

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

Ratio Proportion

Problem

Rose has $350 with her made up of equal number of 25 cents, 50 cents and $1 coins. Find the total number of coins that R has?

  1. 600
  2. 300
  3. 200
  4. 400
  5. 500

The Usual Method

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Let there be ‘x’ number of coins of each denomination. Hence, there are a total of 3x coins.

Total value of each type of coin = 0.25x+0.50x+1x=350

\therefore 1.75x=350

\therefore x=\frac{350}{175}\times 100=200

\therefore Total number of coins that Rose has = 3 x 200 = 600

(Ans: 1)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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We know that the total number of coins will be 3x. Thus the number of coins is a multiple of 3. Only options ‘1’ and ‘2’ are multiples of 3. Hence, the rest are eliminated. Now, check for each 600 and 300 to find the correct answer. This can be done as follows starting with 600:

600 => 200 x 0.25 + 200 x 0.5 + 200 = 50 +100 +200 = 350, so 300 is not the right answer and hence 600 is the correct answer.

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
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