John and his twin brothers each bought three identical notebooks when school started in August. John paid for the notebooks with a $10 bill. He received less than $0.50 in change, all in nickels. No sales tax was charged. What was the price paid for one notebook?
The total cost of all three notebooks was some amount of money less than $10 but greater than $9.50. So we need some amount between those two numbers that is divisible by 0.05 (since all the change was in nickles) AND is divisible by 3 (since this is the price for three books).Originally Posted by aznmartinjai
If we divide $10 by 3, we get $3.333333... (repeats)
If we divide $9.50 by 3, we get $3.1666666... (repeats)
We could use trial and error to see what the amount is by testing numbers between 9.50 and 10.00 that are multiples of 0.05:
$9.55/3 doesn't work
$9.60/3 = $3.20
$9.65/3 doesn't work
$9.70/3 doesn't work
$9.75/3 = $3.25
$9.80/3 doesn't work
$9.85/3 doesn't work
$9.90/3 = $3.30
$9.95/3 doesn't work
There are three answers that work: $3.20, $3.25, $3.30. I'm not sure if I missed something in your explanation of the problem.
ecMathGeek's logic is correct, however, the mistake was he was trying to account for three notebooks when he should have accounted for nine. Recall, John and his twin brothers each bought three identical notebooks. so that's John and two other boys, so that's 3 per boy which is 9 notebooks. so following ecMathGeek's logic of trial and error, we find:
$9.55/9 doesn't work
$9.60/9 = doesn't work
$9.65/9 doesn't work
$9.70/9 doesn't work
$9.75/9 = doesn't work
$9.80/9 doesn't work
$9.85/9 doesn't work
$9.90/9 = $1.10 each notebook
$9.95/9 doesn't work
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