It can be as simple as that:

const sumValues = obj => Object.values(obj).reduce((a, b) => a + b, 0);

Quoting MDN:

The Object.values() method returns an array of a given object's own enumerable property values, in the same order as that provided by a for...in loop (the difference being that a for-in loop enumerates properties in the prototype chain as well).

from Object.values() on MDN

The reduce() method applies a function against an accumulator and each value of the array (from left-to-right) to reduce it to a single value.

from Array.prototype.reduce() on MDN

You can use this function like that:

sumValues({a: 4, b: 6, c: -5, d: 0}); // gives 5

Note that this code uses some ECMAScript features which are not supported by some older browsers (like IE). You might need to use Babel to compile your code.

I know that this question has an accepted answer but I thought I'd chip in with an alternative which uses array.reduce, seeing that summing an array is the canonical example for reduce:

Copy$scope.sum = function(items, prop){
    return items.reduce( function(a, b){
        return a + b[prop];
    }, 0);
};

$scope.travelerTotal = $scope.sum($scope.traveler, 'Amount');

Fiddle

Use Array.prototype.reduce(), the reduce() method applies a function against an accumulator and each value of the array (from left-to-right) to reduce it to a single value.

var array = [{
  "adults": 2,
  "children": 3
}, {
  "adults": 2,
  "children": 1
}];

var val = array.reduce(function(previousValue, currentValue) {
  return {
    adults: previousValue.adults + currentValue.adults,
    children: previousValue.children + currentValue.children
  }
});
console.log(val);