Algebra Smart Math

[Smart Math] Algebra Problem 15

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



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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\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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