MHB Find x and y in x+y=3421 and 23% of x + 13.5% of y = 684.34

[northuk]

I need help with the following problem. I will appreciate any help to solve this:

x+y=3421
23% of x + 13.5% of y = 684.34

What are the values of x and y so the both of above equations give correct answers.

 

[HallsofIvy]

I need help with the following problem. I will appreciate any help to solve this:

x+y=3421
23% of x + 13.5% of y = 684.34

What are the values of x and y so the both of above equations give correct answers.

"23% of x + 13.5% of y = 684.34" is equivalent to the equation
0.23x+ 0.135y= 684.34.

x+ y= 3421 is the same as y= 3421- x so the second equation can be written
0.23x+ 0.135(3421- x)= 684.34.

0.135*3421= 461.835 so that equation is the same as 0.23x+ 461.835- 0.135x= 684.34.

We can write that as (0.23- 0.135)x= 684.34- 461.835 and, doing the arithmetic,
0.095x= 172.505 so x= 172.505/0.095= 1816, approximately. Then y= 3421- x= 3421- 1816= 1605. Again, approximately. I have rounded to the nearest integer. Since one the given data had only 2 significant figures that should be accurate enough.