Question

Help pls
You add the same amount of money to your savings each week. At week 5 you have $45. At week 12 you have $80. How much money do you have at week 20?

Answer 1

Answer: $120

First, create a function

• x = number of week
• y = amount of money in savings
• a = amount of money added each week
• b = the amount of money in savings at week 0

$\left \{ {{5a+b=45} \atop {12a+b=80}} \right.\\\\(5-12)a+(1-1)b=45-80\\\\-7a=-35\\\\a=\frac{-35}{-7} =5\\\\5a+b=45\\\\5(5)+b=45\\\\b=45-25=20$

Therefore, the function is y = 5x + 20

To find the amount of money at week 20, set x = 20 and solve:

$y=5(20)+20=100+20=120$

Therefore, the answer is $120.