There is a quick way to solve problems like this

Algebra Level 2

$\begin{aligned} m\times a\times t & =& \frac {1}{8} \\ m\times a\times h & =& 32 \\ m\times t\times h & =& \frac{1}{3} \\ a\times t\times h & =& 162 \\ \end{aligned}$

Given that $m,a,t,h$ are elements of real numbers that satisfy the equations above. Find the value of $m\times a\times t\times h$ .

See part 2 here and part 4 here .

The answer is 6.

4 solutions

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Omkar Kulkarni
Feb 7, 2015

Mutiplying all four equations, $(math)^{3} = \frac{1}{8} \times 32 \times \frac{1}{3} \times 162$ $(math)^{3} = 216 \Rightarrow \boxed{math=6}$

Indeed, the answer could be 6, but the problem asks for the value of $math$ . I believe mathematics is infinitely valuable.

Caleb Townsend - 6 years, 4 months ago

All four equations, but your solution is pitch perfect. Did the exact same thing.

tytan le nguyen - 6 years, 4 months ago

Mj Santos
Feb 7, 2015

Multiplying all the expressions: $mat=\frac18$ $mah=32$ $mth=\frac13$ $ath=162$

Will get: $mat \times mah \times mth \times ath=m^3a^3t^3h^3=\frac18 \times 32 \times \frac13 \times 162 =216$ $math=\boxed{6}$

Very nice! Hope you keep these series up!

tytan le nguyen - 6 years, 4 months ago

Thanks! Follow me!

MJ Santos - 6 years, 4 months ago

Gamal Sultan
Mar 8, 2015

(mat)(mah)(mth)(ath) = (1/8)(32)(1/3)(162)

(math)^3 = 216

math = 6

Samuel Levi Saints Keys
Feb 19, 2015

See that the product of the 4 equations is m^3xa^3xt^3xh^3 hence math is the cubic root of 27x8=6

There is a quick way to solve problems like this

See part 2 here and part 4 here .

The answer is 6.

4 solutions

Discussions for this problem are now closed

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