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. a) Write an equation that can be used to determine after how many months the boys will owe the same amount.
b) 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.
c) 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.

A = 10 months

B = First part, the two equations:

Ian: y = 1000 - 60x, where x is the number of months and y is the remaining balance owed.

Ken: y = 600 - 20x.

They will be equal at 1000 - 60x = 600 - 20x

Second part: Solve the equation. Note, if you're equation is incorrect, solve it anyway because you will still get some credit!

1000 - 60x = 600 - 20x

1000 = 600 + 40x

400 = 40x

x = 10 months

y = 600 - 20(10) = 600 - 200 = $400 still owed.

C =

Solve Ian's equation for y = 0, when no money is owed.

1000 - 60x = 0

1000 = 60x

x = 16.66666 or 17 months.

Ian will not be paid off 6 months after he and Ken owe the same amount. He will still owe money.

Alternatively, six months after 10 is 16 months,

and y = 1000 - 60(16) = 1000 - 960 = 40. He will still owe $40 at 16 months, so he is not paid off.

60 for the first and 130 for the second

step-by-step explanation:

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