What is a three digit number thats an odd multiple of three and the product of its digits is 24 and is larger than 15 squared?

1 answer:

7 0

The only way 3 digits can have product 24 is
1 x 3 x 8 = 241 x 4 x 6 = 242 x 2 x 6 = 242 x 3 x 4 = 24
So the digits comprises of 1,3,8 or 1,4,6, or 2,2,6, or 2,3,4
To be divisible by 3 the sum of the digits must be divisible by 3.
1+ 3+ 8=12, 1+ 4+ 6= 11, 2 +2 + 6=10, 2 +3 + 4=9Of those sums of digits, only 12 and 9 are divisible by 3.

So we have ruled out all but integers whose digits consist of1,3,8, and 2,3,4.

Meanwhile they must be odd they either must end in 1 or 3.
The only ones which can end in 1 are 381 and 831.

The others must end in 3.

They must be greater than 152 which is 225. So the

First digit cannot be 1. So the only way its digits can contain of1,3,8 and close in 3 is to be 813.

The rest must contain of the digits 2,3,4, and the only way they can end in 3 is to be 243 or 423.
So there are precisely five such three-digit integers: 381, 831, 813, 243, and 423.

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936 jars of peanut butter contain less peanut butter than usual.

Step-by-step explanation:

1. First, we need to find how many jars of peanut butter that contain less peanut butter than advertised are produced every hour.

The factory produces 1200 jars of peanut butter every hour

3.25% of those jars have less peanut butter than advertised

So: multiply $(1200*.0325)$ (the decimal form of the percent) to find the amount of peanut butter jars that contain less peanut butter than advertised.

$(1200*.0325) = 39$

So the factory produces 39 jars of peanut butter that contain less peanut butter than advertised.

2. Second, we need to find how many jars of peanut butter that contain less peanut butter than advertised in three 8 hour work days.

Lets add these work days together to find the total amount of hours: $(8 + 8 + 8) = 24$

So: three 8 hour work days totals to 24 hours

Since the factory produces 39 jars of peanut butter that contain less peanut butter than advertised per hour. Multiply $(24 * 39)$ to find the total amount of jars produced in three 8 hour work days.

$(24 *39) = 936$

A total of 936 peanut butter jars are produced in three 8 hour work days that contain less peanut butter than advertised.

3. If you want to double check your work do the following.

Since the factory produces 1200 jars an hour and 24 hours total three 8 hour work days. Multiply $(1200*24) = 28800$

So there is a total of 28800 jars produced in three 8 hour work days.

Then you can multiply 28800 by 3.25% of jars that contain less peanut butter to find the total amount of peanut butter jars that contain less peanut butter in three 8 hour work days.

$(28800 * .0325) = 936$