Eli is a dental sales representative who wants to distribute 16 brochures and 14 pamphlets to local dental offices. He wants to deliver the same combination of brochures and pamphlets to each office, without having any materials left over. What is the greatest number of dental offices Eli can distribute materials to?

14/16 can be reduced to 7/8

that's about it, he can visit 2 dental offices.

both numbers can't be split up into nicer packets, like 3 or 5. only the 14 is divisible by 7, but not the 16.

this means he can't leaves 3 there, 3 there, because that will leave as rest

other scenario: he throws 2 brochures right into the recycling bin and visits up to 14 dental offices

The answer is two offices are the greatest number he can distribute to.

2 is the reciprocal of 1/2

And 1/2 is our multiplier.

As we are not provided his maximum amount of brochures and pamphlets held, we are given one set of numbers being ratio 16:14

Step-by-step explanation:

16+14 = 30 combined brochures and pamphlets.

1/2 x 16 = 8  brochures maximum each dental office

and 1/2 x 14 = 7 pamphlet maximum each dental office

ratio = 8:7  combination shown as ratio

therefore reciprocal of 1/2 = 2