More variables than equations

Algebra Level pending

Let $r =\dfrac{s}{2}$ , $s=7t$ , $t=2u$ , $u=3v$ , $v= 4w$ , $w=10z$ and $z\neq 0$ .

Find the value of $\dfrac{r+s+t+u+v+w}{z^{3}}$ .

2903 2931 2930 2913

1 solution

Hana Wehbi
Jun 4, 2016

Since all the other variables are build upon $z$ , so use the picking numbers strategy; pick a small number for $z$ and find the values for the rest of the variables. For instance, let $z=1$ then $w=10, v=40, u= 120, t= 240, s= 1680, \text{and} r= 840$ $\implies$

$\Large\frac{r+s+t+u+v+w}{z^{3}}$ = $2930$ by substitution.

Yes , that's it. Did the exact same way.

Aniruddha Bagchi - 5 years ago

Thanks. I found this way is the quickest way to solve it.

Hana Wehbi - 5 years ago

Question, Hana......shouldn't the denominator equal z instead of z^3 in order to achieve 2930 as the correct result? Otherwise, z has to equal unity.

tom engelsman - 4 years, 3 months ago

@Tom Engelsman , the question has the denominator as $z^3$ but when we solved it since we have more variables than equations, plugging a certain value for $z$ was helpful.

Hana Wehbi - 4 years, 3 months ago

More variables than equations

1 solution

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