Question

Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together.
The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?

Answer 1

Hmm.. lets start out by seeing if you have any idea of where the X and Y might go

Answer 2

Anything?

Answer 3

one sec.

Answer 4

kk

Answer 5

x+y=100

0.5x+0.36y=1
??

Answer 6

NICE!.. that was great,

Answer 7

what do i do now?

Answer 8

Add

Answer 9

add?

Answer 10

how?

Answer 11

Do 0.50x +0.36y

Answer 12

x+y=100
+
0.5x+0.36y=1
---------------

Answer 13

Let x = amount of 24% solution
Let y = amount of 50% solution

Total amount of solution made is:
x + y = 100

Amount of solvent in solution:
0.24x + 0.50y = 0.36(100)
24x + 50y = 3600
12x + 25y = 1800

System of equations is:
x + y = 100
12x + 25y = 1800

Answer 14

someone help?!

Answer 15

Solve the first equation for x: x = 100 - y
Now substitute that into the second equation:
12(100 - y) + 25y = 1800
1200 - 12y + 25y = 1800
1200 + 13y = 1800
13y = 600
y = 600/13
y = 46.15 (approximately)

x + y = 100
x + 600/13 = 100
x = 100 - 600/13
x = 1300/13 - 600/13
x = 700/13
x = 53.85 (approximately)

Answer 16

put the amount of 24% solution as \(x\) gallons, then since the total is 100 gallons the amount of 50% solution must be \(100-x\)
you want the ending amount to be 36% of 100 which is 36
set
\[.24x+.5(100-x)=36\] and solve
easier to multiply by 100 and solve
\[24x+50(100-x)=3600\]

Answer 17

\[24x+5000-50x=3600\]
\[-26x=-1400\]
\[x=\frac{1400}{26}\]

Answer 18

You can do a mental calculation by subtracting 24 from 50 to get 26, which is the total of the two portions, in the ratios, 50-36=14. and 36-24=12
The volumes are therefore 100*14/26 and 100*12/26 (for x and y respectively).