Question

Every year Victoria receives $30 for her birthday plus $2 for each year of her age Lacey receives $20 for her birthday and $4 for each year of her age in 2013 Victoria is 10 and Lacey is 6 in what year will they both receive the same amount of money

Answer 1

Solution: 
Let y= the total no. of the years in Lacey's age 
Since the question establishes Victoria as being older than Lacey by 4 years, 
Let y+4 = the total no. of the years of Victoria's age 

We know that Lacey receives $20 on her birthday as well as $4 for every year of her age 
So the total amount she would receive on her birthday is = $20 + $4y 


We know that Victoria receives $30 on her birthday as well as $2 for every year of her age 
So the the total amount she would receive on her birthday is = $30 + $2(y+4) 

Now we want to know how much money Victoria and Lacey would receive individually if both received the same amount of money. 
To do this, we make the total money received by Victoria = to that received by Lacey and vice versa 
So, 
$20 + $4y = $30 + $2(y+4) 
20 + 4y = 30 + 2y + 8 
2y = 18 y = 9 

So, Lacey will be 9 years old when she receives the same amount of money as Victoria and Victoria will be 9+4 = 13 years old when she receives the same amount of money as Lacey. 
Now, in 2013 Lacey is 6 and Victoria is 10. In 3 years time, Lacey will be 9 and Victoria will be 10. 

Therefore the year in which they both receive the same amount of money will be 2016

Answer 2

2018 they will make the same