Math Question

[WLDchild99]

Luke earned $658. He spent some of the money on a new bike. He has about $500 left. He rounded to the nearest hundred to estimate the difference. What are THREE different amounts he might have spent on the bike ?

 

[Steven G]

How much money might he have left? Remember whatever you say for your answer it must round off to 500 when you round off to the nearest hundred.

 

[WLDchild99]

The 1st one I got was 158 (Estimate) - The second one was 200 - Rounding (700 - 500 = 200). What would the 3rd answer be ?

 

[Dr.Peterson]

Luke earned $658. He spent some of the money on a new bike. He has about $500 left. He rounded to the nearest hundred to estimate the difference. What are THREE different amounts he might have spent on the bike ?

The 1st one I got was 158 (Estimate) - The second one was 200 - Rounding (700 - 500 = 200). What would the 3rd answer be ?

Let's look at your answers: If he spent $158, then to estimate how much he'd have left, he would round each number and subtract $700 - 200 = $500 -- good. If he spent $200, he wouldn't have had to round that at all, and would make the same estimate -- good.

But in fact, any number that would round to $200 would work, wouldn't it?

There are many possible answers, not just three. The question is worded that way in order to make sure you think beyond the obvious.

What is the largest amount he might have spent -- the largest number that would round to 200?

What is the smallest amount he might have spent -- the smallest number that would round to 200?

Then pick any three numbers within that region. You have two.

 

[WLDchild99]

Here is what we did. Thanks so much !!

It could have been
$158 =$500 left
$159= $499 left
$109 = $549 left
All of which round to $500
Random amounts would have been correct as long as they still rounded to $500.

 

[Deleted member 4993]

Here is what we did. Thanks so much !!

It could have been
$158 =$500 left
$159= $499 left
$109 = $549 left
All of which round to $500
Random amounts would have been correct as long as they still rounded to $500.

Correct!

However, those "equals to" (=) signs are misplaced. In most of the classes, your grade will be diminished. I would write:

$158 → $500 left
$159 → $499 left
$109 → $549 left

In mathematics, we like "short but precise & accurate" statements.

 

[Dr.Peterson]

Here is what we did. Thanks so much !!

It could have been
$158 =$500 left
$159= $499 left
$109 = $549 left
All of which round to $500
Random amounts would have been correct as long as they still rounded to $500.

As I understand the problem, it is not saying that he rounded his final answer to the nearest 100, as you show (and as I initially took it myself!), but that he rounded both numbers to the nearest hundred before subtracting, as a method of estimating. It says, "He rounded to the nearest hundred to estimate the difference."

So the check that you are correct is:

Spent $158 of $658: estimated 700 - 200 = $500 (actually 658-158=500)​

Spent $159 of $658: estimated 700 - 200 = $500 (but actually 658-159=499)​

Spent $109 of $658: estimated 700 - 100 = $600, which he didn't do (though actually 658-109=549)​

Other correct answers could be

Spent $151 of $658: estimated 700 - 200 = $500 (but actually 658-151=507)​

Spent $249 of $658: estimated 700 - 200 = $500 (though actually 658-109=409, so his estimate is off)​

If I'm right, then part of the point may be that this method of estimation is not always the best.