Official Guide Problem Solving Question 234:
Question:
In a certain game, a large container is filled with red, yellow, green and blue beads worth, respectively 7,5,3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
OG Answer:
From this, the red beads represent factors of 7 in the total point value of 147,000. Since 147,000 = 147(1000), and 1000 = 10 cubed, then 147 is all that needs to be factored to determine the factors of 7. Factoring 147 yields 147 = (3)(49) = (3)(7 squared). This means there are 2 factors of 7, or 2 red beads.
My Question:
The container only contains Red(7), Yellow(5), Green(3) and Blue(2) beads with their respective point value. (I am not saying there are only 7 red beads, 5 yellow beads, etc)
The total point value is 147 thousand --> 147,000
A factor of one thousand is being put aside and is not accounted for because...??....
Could someone explain to me why we are setting aside a factor of 1000 points which corresponds to a quantity of beads and settling for only 2 red beads (7 squared -- 7 being the point value for red beads). The 1000 points corresponds to some quantity of Red, Yellow, Green and Blue beads, since none of the points equate to a value of 10 (from 10 cubed), this point value must be a 'composite' value of some combination of the beads.
What am I not seeing in this problem?
Thank you in advance for your time spent on this problem
Alain
Are the 1000 beads (factored out) a factor of the beads with point value of 5 and 2? -- ie: Green(5) and Blue(2)
Question:
In a certain game, a large container is filled with red, yellow, green and blue beads worth, respectively 7,5,3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
OG Answer:
From this, the red beads represent factors of 7 in the total point value of 147,000. Since 147,000 = 147(1000), and 1000 = 10 cubed, then 147 is all that needs to be factored to determine the factors of 7. Factoring 147 yields 147 = (3)(49) = (3)(7 squared). This means there are 2 factors of 7, or 2 red beads.
My Question:
The container only contains Red(7), Yellow(5), Green(3) and Blue(2) beads with their respective point value. (I am not saying there are only 7 red beads, 5 yellow beads, etc)
The total point value is 147 thousand --> 147,000
A factor of one thousand is being put aside and is not accounted for because...??....
Could someone explain to me why we are setting aside a factor of 1000 points which corresponds to a quantity of beads and settling for only 2 red beads (7 squared -- 7 being the point value for red beads). The 1000 points corresponds to some quantity of Red, Yellow, Green and Blue beads, since none of the points equate to a value of 10 (from 10 cubed), this point value must be a 'composite' value of some combination of the beads.
What am I not seeing in this problem?
Thank you in advance for your time spent on this problem
Alain
Are the 1000 beads (factored out) a factor of the beads with point value of 5 and 2? -- ie: Green(5) and Blue(2)
