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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!!!

Apr 26, 2019

#2
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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.

.

Apr 26, 2019
#3
+1

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.

Apr 26, 2019
#4
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That's a good solution BUT the original poster requested a solution using a method other than algebraic.

non-algebraic

Guest Apr 29, 2019