Three bank accounts are opened and then have fixed amounts of money withdrawn each month. The points graph (2, 50) (4, 20) shows Account A. The table:
Month 1 - $100 left
Month 2 - $75 left
Month 3 - $50 left
Month 4 - $25 left
represents Account B, and the equation y=-22.5x+90 represents Account C, where y represents the amount of money (in dollars) left after x months.
Which account has the greatest initial value? Which has the least initial value?
Which account has the most amount of money withdrawn each month? Which has the least amount?
Which account runs out of money first? Which account runs out of money last?
The initial value of an account is the amount of money left in the account at month 1.
For Account A, at month 1 there is $100 left. Therefore, the initial value of Account A is $100.
For Account B, at month 1 there is $100 left. Therefore, the initial value of Account B is also $100.
For Account C, the equation y=-22.5x+90 represents the amount of money left after x months. Substituting x=1 into the equation, we get y=-22.5(1)+90=90-22.5=67.5. Therefore, the initial value of Account C is $67.50.
Therefore, Account A and Account B have the greatest initial values, while Account C has the least initial value.
To determine the amount of money withdrawn each month, we need to calculate the difference between the amount left in each account from month to month.
For Account A, the difference between the amount left in month 1 and month 2 is $100-$75=$25.
The difference between the amount left in month 2 and month 3 is $75-$50=$25.
The difference between the amount left in month 3 and month 4 is $50-$25=$25.
Therefore, Account A has a fixed withdrawal of $25 each month.
For Account B, the difference between the amount left in month 1 and month 2 is $100-$75=$25.
The difference between the amount left in month 2 and month 3 is $75-$50=$25.
The difference between the amount left in month 3 and month 4 is $50-$25=$25.
Therefore, Account B also has a fixed withdrawal of $25 each month.
For Account C, the equation y=-22.5x+90 represents the amount of money left after x months. The coefficient of x (-22.5) gives the change in y for each one month increase in x. Therefore, Account C has a withdrawal of $22.50 each month.
Therefore, Account A and Account B have the most amount of money withdrawn each month, while Account C has the least amount.
To determine which account runs out of money first, we need to compare the amount left in each account at month 4.
For Account A, at month 4 there is $25 left.
For Account B, at month 4 there is $25 left.
For Account C, substituting x=4 into the equation y=-22.5x+90, we get y=-22.5(4)+90=90-90=0. Therefore, Account C runs out of money first.
To determine which account runs out of money last, we need to compare the amount left in each account at month 1.
For Account A, at month 1 there is $100 left.
For Account B, at month 1 there is $100 left.
For Account C, substituting x=1 into the equation y=-22.5x+90, we get y=-22.5(1)+90=90-22.5=67.5. Therefore, Account C runs out of money last.