Question

A chemist mixes some 70% solution with some 40% solution to obtain 120 gallons of 50% solution. Find the number of gallons of each solution.

A. define variables for unknown
B. write a system of equations to model the problem
C. Solve System
D. Give answer in a sentence

Answer 1

---> x + y = 120

---> 70x + 40y = 50(120)

Answer 2

A. unknown variables : x + y = 120 ?
B. system of equations : 70x + 40y = 50 (120) ?
@dumbcow

Answer 3

do you know what a variable is?

Answer 4

x and y

Answer 5

very good... those are variables because they represent unknown values, namely the number of gallons for 70%solution and 40%solution

a system of equations implies more than 1 equation
we have 2 equations in our system

Answer 6

and the equations are x + y = 120
70x + 40y = 50 (120)

Answer 7

yes

Answer 8

solve by using substitution

x+y = 120 ---> y = 120 - x

70x + 40(120-x) = 50(120)

solve single equation for x

Answer 9

x = 70?

Answer 10

nope

Answer 11

1.25?

Answer 12

I did 70 (0) + 40 (120-0) = 50 ( 120)

Answer 13

?? that is assuming x=0 , not finding what x actually is

Answer 14

I thought thats what substituting was

Answer 15

how do i find x then?

Answer 16

i kinda helped by doing the substitution for you

i solved for y in 1st equation ----> y = 120-x
and plugged it into 2nd equation ..... replaced "y" with "120-x"

think back to when you first learned algebra, you want to isolate the variable
step 1: distribute the 40(120-x)
step 2: add like terms
step 3: get "x" term on left side, constant on right side
step 4: divide

Answer 17

oh yea that makes sense now