How to write an equation to represent minnies allowance

Question

Minnie and Max are twins. Each of them receives a $5.00 allowance. Minnie wants her allowance to increase by $2.00 each year. Max wants his allowance to increase by 30 percent each year. 

1. Write an equation to represent Minnie's allowance.
2. Write an equation to represent Max'a allowance. 
3. Complete the given table for both Minnie and Max. 

Answer 1

This problem compares an arithmetic sequence with a geometric sequence.

 

Minnie:

a_n = 5 + (n - 1)(2.00)

a_n = 5 + 2.00n - 2.00

a_n = 3 + 2.00

 

Max:

a_n = 5(1.3)^n-1

Answer 2

I'm thinking this problem should be stating an amount per week instead of per year.  A $2 increase per year is next to nothing.  Assuming the allowances and increases are "per week," I can give you an explanation.

 

"Per", "each", and "every" usually indicate multiplication in an equation.  The equation for their original equation would be something like y = 5x. 

 

Since Minnie wants to increase hers by 2, she wants $2 more each week, which would be $7 each week.

y = 7x

 

Max is a little more complicated.  His original allowance can be considered 100%.  Adding 30% to it would be 130%.  To find the percent, move the decimal two places to the left to get 1.30 and multiply.  5(1.30) = 6.50

 

Max's new equation could be 6.50x.

 

On Minnie's table, just multiply by 7.  Max's table, multiply by 6.50.

 

Hope this helps!