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# [Smart Math] Algebra Problem 8

Here’s and example of a SMART MATH problem for 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

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

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