All of the attendees at a symposium are either phys- icists or biologists. If there are 123 physicists and
270 biologists, then how many additional physicists
must arrive at the symposium in order for the ratio
of physicists to total attendees to become 2 to 5?

The number of additional physicist that must arrive are;

59 physicists

Explanation:

A ratio in mathematics is an indication of the number of times one quantity is larger than another quantity, that is the number of times a number of an item is found the number of another item

The given parameters of the attendees at the symposium are;

The number of physicists at the symposium, p = 123 physicists

The number of biologists at the symposium, b = 270 biologists

The total number of attendees at the symposium, T = 123 + 270 = 393 attendees

Let 'x' represent the expected number of physicist at the symposium

For the ratio of physicists to the total attendees to become 2:5, we have;

x/Tₓ = 2/5

Where;

Tₓ = The expected total number of attendees at the symposium = x + 273

∴ x = (2/5) × Tₓ  = (2/5) × (x + 273)

x = (2/5) × (x + 273) = 2·x/5 + 2×273/5

x - 2·x/5 = 2×273/5

3·x/5 = 2×273/5

3·x = 546

x = 546/3 = 182

The expected number of physicist at the symposium, x = 182 physicist

The number of additional physicist that must arrive = x - p

∴ The number of additional physicist that must arrive = 182 - 123 = 59

The number of additional physicist that must arrive = 59 physicists