Problem Solving

The sum of X and Y's ages is 105. When X was Y's age, she was one and a half times Y's age. What are there present ages.?

First we have to look closely at the information.

The Sum of X and Y is 105, So X+Y=105

When X was Y's age she/he was 1 and 1/2 times her/his age. So pick an even number to figure it out, in this case 10 years old.

So, if X is 1 and 1/2 times Y's age that when Y was 10 years old, X was 25<------10+10(one) + 5 (half or 1/2).

Then plug and play or multiply

if X is 75 years old then Y has to be 30 years old. 75+30=105

HX83 wrote:First we have to look closely at the information.

The Sum of X and Y is 105, So X+Y=105

When X was Y's age she/he was 1 and 1/2 times her/his age. So pick an even number to figure it out, in this case 10 years old.

So, if X is 1 and 1/2 times Y's age that when Y was 10 years old, X was 25<------10+10(one) + 5 (half or 1/2).

Then plug and play or multiply

if X is 75 years old then Y has to be 30 years old. 75+30=105

Ha-Ha

I should have known that 1,5 times = 1+1+1/2

The problem asks the present ages and explanation above does operate with the past age information.


Anyway leave it to me

let's assign values A1=X (past) and A2=X (present), B1=Y (past) and B2=Y (present), further we map the events

In the past ............ A1 .......... B1
Now ....................... A2 .......... B2

according to the problem...when X was Y's age, she was one and a half times Y's age

when A1=B2 (this is the only possible logical chain of events!) then A1=1,5*B1

also, we are given ... the sum of X and Y's ages is 105 - i.e. A2+B2=105

since time passed from the past events should be equal for [A1 through A2] and [B1 through B2], the left and right sides in the map above should be vertically equal (and how? see below)

A2-A1=B2-B1

Now it's time for variable conversions and setting equations:
copy/paste

{A1=B2
{A1=1,5*B1

Supply all conversed values into these equations
A2-A1=B2-B1;
A2+B2=105


{A2-1,5*B1=1,5*B1-B1
{A2+B2=105;

{(105-1,5*B1) - 1,5*B1=1,5*B1-B1; 105-3*B1=0,5*B1;
{A2=105-B2; A2=105-1,5*B1

105-3*B1=0,5*B1 <> 105=3,5*B1 <> B1=30

A1=30*1,5; A1=45

A1=B2; B2=45

A2+B2=105; A2=105-45; A2=60

The present ages are following:

X = 60 and Y = 45

Let's check

A1=45..........B1=30
A2=60..........B2=45

Correct!