Question

Two boxes contained 155 lb of flour. If you take 20 lb from the first and add it to the second, the first box will contain 12 19 of what is now in the second. What amount of flour was originally in each box

Answer 1

Answer:

First and second box had 80 and 75 lb flour originally.

Step-by-step explanation:

Let the two boxes contained x lb and y lb of the flour respectively.

Both the boxes contained 155 lb of flour in total.

So the first equation will be,

x + y = 155 --------(1)

If the 20 lb of the flour is taken out then amount of flour in first box = (x - 20) lb

and added to the second box then flour in second box = (y + 20) lb

After the mixing of flour statement says that "the first box will contain $\frac{12}{19}$ of the flour now in the second box."

For this statement equation will be

$(x-20)=\frac{12}{19}(y+20)$

19(x - 20) = 12(y + 20)

19x - 12y = 380 + 240

19x - 12y = 620 ------(2)

Equation (1) × 12 + equation (2)

12(x + y) + (19x - 12y) = 155×12 + 620

31x = 1860 + 620

31x = 2480

x = $\frac{2480}{31}$

x = 80 lb

from equation (1)

80 + y = 155

y = 155 - 80

y = 75 lb.

Therefore, first and second boxes had 80 lb and 75 lb of flour originally.