Mia's Mathematical Mishap

[BMAD]

Mia needed to calculate the volume of a rectangular room. She multiplied the length andthe width correctly but the width had been incorrectly written down, it was one-third larger than it should have been. To make up for this, she lowered the height by one-third, then multiplied it on. She figured this was okay since the width was equal to the height. She then found her volume was off by 20 cubic meters. Why was Mia wrong, and what

was the actual volume?

[bonanova]

L x (4/3)W x (2/3)H = (8/9) V = V - 20

(1/9)V = 20

V = 180

She should have multiplied the (too large) width by (3/4)