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# [Smart Math] Algebra Problem 23

Here’s and example of a SMART MATH problem for 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

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

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 = $3\times 1152\approx 3300$(+).