Math help please

Question

You need to order pipe for 3 different projects which require 42, 126, and 210 feet of pipe respectively. Pipes can be ordered any length, however, all pipes in an order must be of the same length. Pipes may be combined to produce longer pipes, but may not be cut. What size of pipe would result in the smallest order size?

Answer 1

It's not clear what you mean by "smallest".  Do you mean smallest total length of pipe, or smallest number of pipes?

 

Anyway, since 126 and 210 are both multiples of 42, then you'd do well to order pipes in 42 foot lengths.  Then you could order 1 pipe for the first job, 3 pipes for the second job, and 5 pipes for the third. 

 

This is a problem where you're being asked to find the greatest common divisor of the three numbers.

 

 

 

Answer 2

write the prime factorization for each number

42=2x3x7

126=2x3x3x7

210=2x3x5x7

find the greatest common factor (GCF) for the three numbers

GCF=2x3x7=42

you can buy 1 42 foot pipe for the 42' project

you can buy 3 42 foot pipes for the 126' project

you can buy 5 42 foot pipes for the 210' project

you buy 9 42 foot sections of pipe

you said in the previous answer that the choices were 7, 14, 150, and 200

what do you mean by "the smallest order size" ?

you can buy 6 7s, 18 7s, and 30 7s for a total of 54 7s, or...

you can buy 3 14s, 9 14s, and 15 14s for a total of 27 14s

you choose the answer that best fits the problem