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
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