Problem Solving

BTGmoderatorLU wrote:Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains two pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?

A. 6
B. 12
C. 20
D. 24
E. 120

We have 240 pounds of the seed mixture, and 5% of the mixture is timothy.
So: TOTAL weight of timothy = 5% of 240 pounds
= 12 pounds

So, we there are 12 pounds of timothy in the mixture, and 2 pounds of timothy is needed for 1 acre
This means 4 pounds of timothy is needed for 2 acres
And 6 pounds of timothy is needed for 3 acres
And 12 pounds of timothy is needed for 6 acres

Answer: A

BTGmoderatorLU wrote:Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains two pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?

A. 6
B. 12
C. 20
D. 24
E. 120

5% of the total seed mixture n contains 2 pounds of timothy, so we have:

0.05n = 2

n = 2/0.05 = 200/5 = 40 pounds of mixture

We can create a proportion in which a = the number of acres that can be planted with 240 pounds of the seed mixture:

40/1 = 240/a

40a = 240

a = 6

Alternate Solution:

We note that there are 240 x 5% = 240 x 0.05 = 12 pounds of timothy in 240 pounds of seed mixture. Since one acre needs to contain 2 pounds of timothy, we can plant 12/2 = 6 acres with 240 pounds of seed mixture.

Answer: A