Can some explain to me why my numbers are getting added like strings and not numbers? Am I using parseInt incorrectly?

I created a variable named firstScore and then defined it using a prompt, I then immediately converted the prompt string to a number using parseInt. I did the same for secondScore, then added them in a new variable named totalScore. When I add firstScore and secondScore it gets read like a string, however if I add a variable with a number for exmaple like firstScore + 100, it gets read like a number. I'm confused do I need to manually convert every string number individually with parseInt to get it to work consistently? The top program works correctly and the bottom one doesn't, help would be greatly appreciated.

console.log("start program");
var age= prompt("how old are you?");
age=parseInt(age);
var score=100;
alert(age+score);
console.log("program ended");

console.log("start program");
var firstScore= prompt("what was your first score");
fisrtScore= parseInt(firstScore);
var secondScore= prompt("what was your second score");
secondScore= parseInt(secondScore);
var totalScore= secondScore + firstScore;
alert("your total score is " + totalScore + "!");
console.log("program ended");