Question 342862
The ratio of students who ride the bus to the students who do not ride the bus is 7 to 3. If 490 students ride the bus, how many students do not ride the bus?


Since the ratio of riders to non-riders is 7:3, then {{{7/10}}} are riders and {{{3/10}}} are non-riders


Using N for non-riders, and since there are 490 riders, or {{{7/10}}} of total riders, and we need to know what number represents non-riders, or {{{3/10}}} of total riders, we can say that:


{{{(7/10)/(3/10) = 490/N}}}


Cross-multiplying, we get: {{{(7N/10) = 147}}}


Cross-multiplying again, we get: 7N = 1,470


N, or non-riders = {{{1470/7}}} or {{{highlight_green(210)}}} students.


METHOD II
We could have also done it the shortcut way by noticing that the riders' ratio of 7 was multiplied by 70 to get the total amount of riders, 490 (7 * 70).


Therefore, we can also multiply the non-rider ratio of 3 by 70 to get {{{highlight_green(210)}}} (3 * 70), or simply put:

{{{highlight_green((7*70)/(3*70) = 490/210)}}}