Question

A person's intelligence quotient (i) is found by dividing mental age (m), as indicated by standard tests, by chronological age (c), and then multiplying this ratio by 100. the formula i = 100m c can be used. if the i range of a group of 12-year-olds is given by 80 ≤ i ≤ 120, find the range of the mental age of this group. (enter your answers from lowest to highest.)

Answer 1

$9.6 \leqslant m \leqslant 14.4$
i = (100m)/c
lowest i = 80, highest i = 120
c = 12
this will result in 2 equations, one will be the lowest (solving m when i = 80), and the highest (solving m when i = 120)
solve m when i = 80:
i = (100m)/c
80 = (100m)/12
80×12 = 100m
960 = 100m
960/100 = m
9.6 = m
solve m when i = 120:
i = (100m)/c
120 = (100m)/12
120×12 = 100m
1440 = 100m
1440/100 = m
14.4 = m
therefore,
$9.6 \leqslant m \leqslant 14.4$