earning money

Question

on the 8th day of summer ,ricky had $212 in his bank account. on the 40th day of summer, he had $852.

 

1) how much money did he have on the 20th day?

2) after how many days would he have $1,000?

3) what assumptions did you make when solving this problem? explain.

Answer 1

OK, you'll still be alive on Monday.

3) I'll assume that he puts in the same amount each day.

1) Using an arithmetic sequence

 

a₄₀ = a₈ + (32)d               40 - 8 = 32

852 = 212 +(32)d            substitute

640 = 32d                        subtract 212 from both sides

20 = d                              divide both sides by 32

 

He adds $20 each day.

 

2)

1000 = 212 + (n - 1)(20)

 

Now solve for n.