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Algebra Smart Math

[Smart Math] Algebra Problem 23

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

Algebra

Problem

In a school in which 40% of the enrolled students are boys, 80% of the boys are present on a certain day. If 1152 boys are present, the total school enrollment is _______.

  1. 1440
  2. 2880
  3. 3600
  4. 5400
  5. 5760

The Usual Method

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Let the total enrollment be ‘x’.

Hence total number of boys = 40% of x = 0.4x.

Total number of boys present = 80% of boys = 0.8\times 0.4x=0.32x

Also total number of boys present = 1152

\therefore 0.32x=1152

\therefore x=\frac{1152}{0.32}=3600

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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We know that 80% of the boys present out of the total 40% boys make 0.32x = 1152.

We also know that 1/3 = 0.33. Hence we can approximate 0.32 as 0.33 and so 1152 is approximately 1/3 of the total enrollment. Hence total enrollment = 3\times 1152\approx 3300(+).

(Note: The ‘+’ sign indicates that the answer is slightly greater than 3300).

From the options we see that 3600 is the only one closest to 3300 and greater than that. Hence, 3600 is the answer.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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