Problem Solving

In question 234 of OG11 I don’t like the explanation of the solution. Can someone please help?

Question:
In a certain game, a large container is filled with red, yellow, green and blue beads, worth 7, 5, 3, 2 points each. A number of beads are then removed from the container. If the product of the values of the removed beads is 147,000, how many red beads were removed?

Now my first question is why is only 147 considered? The solution almost excludes 147 or 147(1000). Why?

Second question, if you do accept that you only need to consider 147, why do you need factor 147 to determine the factors of 7 / which reveals 2 factors (3 & 7)

What if the question asked you how many green beads or blue beads were removed? What would you factor then?

Thanks so much!

T_A_M wrote:In question 234 of OG11 I don’t like the explanation of the solution. Can someone please help?

Question:
In a certain game, a large container is filled with red, yellow, green and blue beads, worth 7, 5, 3, 2 points each. A number of beads are then removed from the container. If the product of the values of the removed beads is 147,000, how many red beads were removed?

Now my first question is why is only 147 considered? The solution almost excludes 147 or 147(1000). Why?

Second question, if you do accept that you only need to consider 147, why do you need factor 147 to determine the factors of 7 / which reveals 2 factors (3 & 7)

What if the question asked you how many green beads or blue beads were removed? What would you factor then?

Thanks so much!

Ok so we know the following information.

red = 7 points
yellow = 5 points
green = 3 points
blue = 2 points.

Now the product of all of the values of the beads removed is 147,000

So let's prime factor 147,00 and see what we come up with.

147000 = 147 * 1000

147 = 7 * 21 = 7^2 * 3
1000= 100 * 10 = 10 * 10 * 10 = 5^3 * 2^3

So, 147,000 = 2^3 * 3 * 5^3 * 7^2

So we would have: 2 reds, 3 yellows, 1 green, and 3 blues.


The reason you can disregard the 1000 in this problem is because 1000 doesn't have a factor of 7 in it.