This week, the Zweezam Factory sold 32 parts altogether. They sold half as many Zweedulls as Zweenubs and one-fifth as many Zweebuds as Zweedulls. How many of each type did the factory sell?

1 Answer
Ms. Worth
Mar 25, 2018

#color(white)(h)##2  "Bubs"#

#10   "Dulls"#

#20  "Nubs"#

Explanation:

Problems like this are confusing because it's hard to find a good way to express the number of each kind of parts.

It's really helpful to describe these numbers all in terms of the same variable,

So let #10x# represent the number of #"Nubs"#

#"Nubs"# . . . . . . . . . . . . . . . . #10x# #larr# number of #"Nubs"#
One half of #"Nubs"# . . . . . . .#5x# #larr# number of #"Dulls"#
One fifth of #"Dulls"# . . . . . . #1x# #larr# number of #"Bubs"#

The sum of all these parts equals #32#
#[ "Nubs" ] + [ "Dulls" ] + [ "Bubs" ] = 32#
#[ 10x  ] + [  5x  ] + [   x    ] = 32#

#10x + 5x + x= 32#
Solve for #x#, already defined as "the number of #"Bubs"#"

1) Combine like terms
#16x = 32#

2) Divide both sides by #16# to isolate #x#, already defined as "the number of #"Bubs"#"
• #x = 2# #larr# answer for "the number of #"Bubs"#"

• If #x=2# (which is "the number of #"Bubs"#"),
then the number of #"Dulls"#, (which is #5x#), must be #10#

• If the number of #"Bubs" # is #10#,
then the number of #"Nubs"# must be #20#

#color(white)(mmmmmmmm)#―――――――――

Answer

#color(white)(h)##2  "Bubs"#

#10  "Dulls"#

#20  "Nubs"#

#color(white)(mmmmmmmm)#―――――――――

Check

#"Bubs" . . . . . . 2#

#"Dulls" . . . . . 10#

#"Nubs" . . . . . 20#
#color(white)(mmmnm)#――
#color(white)(mmmmmj)##32# parts altogether

#Check#

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