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# [Smart Math] Algebra Problem 15

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

### Problem

If $\frac{5}{3}+5+\frac{3}{5}+x=7$, what is x?

1. ${}^{4}\!\!\diagup\!\!{}_{15}\;$
2. $-{}^{4}\!\!\diagup\!\!{}_{5}\;$
3. ${}^{3}\!\!\diagup\!\!{}_{5}\;$
4. $-{}^{4}\!\!\diagup\!\!{}_{15}\;$
5. ${}^{2}\!\!\diagup\!\!{}_{3}\;$

### The Usual Method

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$\frac{5}{3}+5+\frac{3}{5}+x=7$

$\therefore x=7-\frac{5}{3}-5-\frac{3}{5}$

$\therefore x=\frac{105-25-75-9}{15}$

$\therefore x=-\frac{4}{15}$

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

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Observe that in the equation $\frac{5}{3}+5+\frac{3}{5}>7$.

Hence x has to be negative number. Also because the denominators are 3 and 5, the denominator of x will be LCM of 3 and 5, i.e. 15. Since only option ‘4’ satisfies the conditions of the denominator being negative as well as =15, it should be the answer.

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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