SAT Math Problem (16)

Question

In the United States, 55 million computers, 32 million televisions, and 150 million cellphones were either disposed of or recycled in the past year. If 30% of computers, 20% of televisions, and 10% of cellphones were recycled, and the average weight of a television is twice the average weight of a computer and 100 times the average weight of a cellphone, what is the approximate percentage by weigh of recycled electronics made up of cellphones?

Answer 1

In the United States, 55 million computers, 32 million televisions, and 150 million cellphones were either disposed of or recycled in the past year. If 30% of computers, 20% of televisions, and 10% of cellphones were recycled, and the average weight of a television is twice the average weight of a computer and 100 times the average weight of a cellphone, what is the approximate percentage by weigh of recycled electronics made up of cellphones?

 

Let c be the average weight of the computer,

      t be the average weight of the television,

      p be the average weight of the cellphones.

 

From the information in the problem, t = 2c = 100p.

This then means that c = .5t and p = .01t

 

The number of recycled computers is .3 * 55 *10⁶ = 16.5 * 10⁶,

which has an average weight of 16.5 * 10⁶ * .5t = 8.25 * 10⁶  * t

 

The number of recycled televions is .2 * 32 *10⁶ = 6.4* 10⁶,
which has an average weight of 6.4 * 10⁶ * t

 

The number of recycled cellphones is .1* 150 *10⁶ = 15 * 10⁶,
which has an average weight of 15 * 10⁶ * .01t = .15 * 10⁶ * t

 

The average weight of the all the recycled electronics is

(8.25 + 6.4 + .15) * 10⁶ * t = 14.8 * 10⁶ * t

 

∴ The percentage of recycled cellphones by weight is

   (.15 * 10⁶ * t)/(14.8 * 10⁶ * t) ≈ 0.01 or 1%