+19 Ian is borrowing $1000 from his parents to buy a notebook computer. He plans to pay them back at the rate of $60 per month. Ken is borrowing $600 from his parents to purchase a snowboard. He plans to pay his parents back at the rate of $20 per month.
1. Write an equation that can be used to determine after how many months the boys will owe the same amount.
2. Determine algebraically and state in how many months the two boys will owe the same amount. State the amount they will owe at this time.
3. Ian claims that he will have his loan paid off 6 months after he and Ken owe the same amount. Determine and state if Ian is correct. Explain your reasoning.
DO NOT LISTEN TO THE ALGEBRAIC PART!!!!
SOLVE ANY WAY JUST NOT THE FIRST WAY THAT WE ALL KNOW!!!
Determine algebraically and state in how many months the two boys will owe the same amount. State the amount they will owe at this time. DO NOT LISTEN TO THE ALGEBRAIC PART
You could make a table, containing each person's amount owed.
Month IAN amount owed KEN amount owed
0 1,000 600
1 940 580
2 880 560
3 820 540
Continue subtracting payments until you get to the month where the two owed balances are the same.
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1 - Let the number of months when they equalize =m
1000 - 60m =600 - 20m, solve for m.
Move the terms with m to the LHS:
-60m + 20m =600 - 1000
-40m = -400
Divide both sides by -40:
m = -400 / -40
m = 10 - months when the 2 boys will owe the same amount.
2 - 1000 - [10 x 60] =$400 - This is the amount they both owe after 10 months.
3 - 6 x $60 =$360 - Ian's claim in not true. It will take him: $400 / $60 = 6 2/3 = ~ 7 months to pay off the remaining balance of $400.
