1. I am a three-digit number. My tens digit is 3 more than my ones digits. If you round me to the nearest ten and subtract
320, the estimated difference is 150. What number am I?

2. I am a three-digit number. All my digits are odd numbers.
My ones digits is 4 more than the hundreds digits. My tens
digits is the greatest of the three digits. If you round me to
the nearest hundred and subtract 100, the estimated
difference is 300. What number am I?

1. 474

2. 397

Step-by-step explanation:

1. If the three-digit number is xyz, then y = z + 3.

When rounded to the nearest ten and reduced by 320, the result is 150.  150 + 320 = 470, so x = 4.  y = 6 if z ≥ 5, and y = 7 if z < 5.

So the number is either 463 or 474.  463 doesn't round to 470, so the answer is 474.

2. If the three-digit number is xyz, then z = x + 4.  y is the largest of the three digits; since all the digits are odd, y is either 5, 7, or 9.  So z is either 5 or 7, and x is either 1 or 3.

When rounded to the nearest hundred and reduced by 100, the result is 300.  100 + 300 = 400, and y > 5, so xyz is rounded up to 400, which means x = 3.  So z = 7 and y = 9.

The answer is 397.

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.