{% extends "percentage_word_problems_1.html" %}


{% block maincell %}
<script language=Javascript1.2><!--

/***
Age word problems
***/


eval("type"+getRandomIntRange(1,5)+"()");  //Randomly choose a problem type


function type1() {
//Solve for the older person's age today
C = getRandomIntRange(2,5);
B = getRandomIntRange(2,20);
A = getRandomIntRange(1,10)*(C-1);
correctAnswer = (C*(-B-A)+B)/(1-C);
write_text('<B>'+person1+' is '+A+' years older than '+person2+'.  '+B+' years ago, '+person1+' was '+C+' times as old as '+person2+'.  How old is '+person1+' today?</B>');
write_step('Let `x=`'+person1+'\'s current age.');
write_step('Then '+person2+'\'s current age would be `x-'+A+'`.');
write_step(B+' years ago, '+person1+' was `x-'+B+'` years old.');
write_step(B+' years ago, '+person2+' was `(x-'+A+')-'+B+'` years old.  That simiplifies to `x'+format_constant(-A-B)+'`.');
write_step('We also know that '+B+' years ago, '+person1+' was '+C+' times as old as '+person2+' so:<center>`x-'+B+'='+C+'(x'+format_constant(-B-A)+')`</center>');
write_step('<center>`x-'+B+'='+format_first_coefficient(C)+'x'+format_constant(C*(-B-A))+'`</center>'+
		'<center>`x='+format_first_coefficient(C)+'x'+format_constant(C*(-B-A)+B)+'`</center>'+
		'<center>`'+format_first_coefficient(1-C)+'x='+(C*(-B-A)+B)+'`</center>'+
		'<center>`x='+(C*(-B-A)+B)/(1-C)+'`</center>');	
}


function type2() {
//Solve for the younger person's age
C = getRandomIntRange(2,5);
B = getRandomIntRange(1,20);
A = getRandomIntRange(1,10)*(C-1);
correctAnswer = A/(C-1);
write_text('<B>'+person1+' is '+C+' times as old as '+person2+'.  '+person1+' is also '+A+' years older than '+person2+'.  How old is '+person2+'?</B>');
write_step('Let `x=`'+person2+'\'s age.');
write_step('Then '+person1+'\'s age is `'+format_first_coefficient(C)+'x`.');
write_step(''+person1+'\'s age could also be written as `x+'+A+'`.');
write_step('So:<center>`'+format_first_coefficient(C)+'x = x+'+A+'`</center>');
write_step('<center>`'+format_first_coefficient(C-1)+'x = '+A+'`</center>'+
		'<center>`x = '+(A/(C-1))+'`</center>');
}	
		
		

function type3() {
A = getRandomIntRange(2,5);
C = getRandomIntRange(A+1,10);
B = getRandomIntRange(2,20)*(C-A);
correctAnswer = (C-1)*B/(C-A);
write_text('<B>'+person1+' is '+A+' times as old as '+person2+' is today. '+B+' years ago, '+person1+' was '+C+' times as old as '+person2+'.  How old is '+person2+' today?</B>');
write_step('Let `x=`'+person2+'\'s age today.');
write_step('Then '+person1+'\'s age  today is `'+A+'x`.');
write_step(B+' years ago, '+person2+'\'s age was `x-'+B+'`.');
write_step(B+' years ago, '+person1+'\'s age was `'+A+'x-'+B+'`.');
write_step('We know that '+B+' years ago, '+person1+' was '+C+' times as old as '+person2+' so:<center>`'+C+'(x-'+B+')='+A+'x-'+B+'`</center>');
write_step('<center>`'+C+'x-'+(C*B)+'='+A+'x-'+B+'`</center>'+
		'<center>`'+C+'x='+A+'x'+format_constant((C-1)*B)+'`</center>'+
		'<center>`'+(C-A)+'x='+((C-1)*B)+'`</center>'+
		'<center>`x='+((C-1)*B/(C-A))+'`</center>');
}


function type4() {
A = getRandomIntRange(2,20);
B = getRandomIntRange(1,5)*(A-1);		
correctAnswer=B/(A-1);		
write_text('<B>In '+B+' years, '+person1+' will be '+A+' times as old as '+pronoun1+' is today.  How old is '+person1+' today?</B>');
write_step('Let `x=`'+person1+'\'s current age.');
write_step('In '+B+' years, '+person1+'\'s age will be `x+'+B+'`.');
write_step('We know that in '+B+' years, '+person1+' will be '+A+' times as old as '+pronoun1+' is today so:<center>`x+'+B+'='+A+'x`</center>');
write_step('<center>`x='+(B/(A-1))+'`</center>');
}

function type5() {

C = getRandomIntRange(2,5);
B = getRandomIntRange(1,10)*(C-1);
A = getRandomIntRange(C*B/(C-1)+1,15)*(C-1);
correctAnswer = (A-(C*B))/(C-1);
	
write_text('<B>'+person1+' is '+A+' years old. '+person2+' is '+B+' years old.  How many years will it take for '+person1+' to be exactly '+C+' times as old as '+person2+'?</B>');
write_step('Let `y=` the years it will take for '+person1+' to be '+C+' times as old as '+person2+'.');
write_step('In `y` years, '+person1+' will be `'+A+'+y` years old');
write_step('In `y` years, '+person2+' will be `'+B+'+y` years old');
write_step('In `y` years, '+person1+' will be '+C+' times as old as '+person2+' so:<center>`'+A+'+y='+C+'('+B+'+y)`</center>');
write_step('<center>`'+A+'+y='+(C*B)+'+'+C+'y`</center>'+
		'<center>`'+(A-(C*B))+'+y='+C+'y`</center>'+
		'<center>`'+(A-(C*B))+'='+(C-1)+'y`</center>'+
		'<center>`'+(A-(C*B))/(C-1)+'=y`</center>');

}


//-->
</script>

{% endblock maincell %}