Ratios question

Question

Individual bags of sand and concrete in a ratio of 2/3 totals 1000 lbs. If you add X number bags of sand, and the new ratio is 4/5, how many bags of sand is X?

Answer 1

The definition of this problem is problematic. First note that the 1000lbs is irrelevant as the units are inconsistent with ratios. The ratios are independent of pounds. Second the number of bags is not relevant as they are independent of the ratios. So we have (S+X)/C=4/5 or one equation in three unknowns S/C+X/C=4/5 with S,C,X integer. There are multiple answers one can find by inspection such as =20,C=30,X=4, or C=5,S=1,X=3. Note also that S is a multiple of 10 and C is a multiple of 15. I suspect an expert in number theory could produce some interesting relationships and quickly give answers.

Answer 2

Assume that the bags each weigh 1 pound.

 

Since the ratio of bags of sand to bags of concrete is 2/3, the number of bags of sand is 2a and the number of bags of concrete is 3a, for some number, a.  

 

2a + 3a = 1000

 

5a = 1000

 

a = 200

 

Number of bags of sand = 2a = 400

Number of bags of concrete = 3a = 600

 

If we add X one pound bags of sand and the ratio of sand bags to concrete bags  is then 4/5, we have:

 

(400 + X)/600 = 4/5

 

Cross multiply:  5(400 + X) = 2400

 

                           2000 + 5X = 2400

 

                                         5X = 400

 

                                           X = 80