Question

six gallons of a salt solution consists of 35 % salt. it is the result of mixing a 40 % solution with a 30 % solution. how many gallons of each of the solutions was used? let x = the number of gallons of the 40 % solution and y = the number of gallons of the 30 % solution. the corresponding modeling system is \\(\

$$\begin{cases} x + y = 6 \\\\ 0.4x + 0.3y = 0.35(6) \\end{cases}$$

\\). solve the system by using the method of substitution. answer how to enter your answer (opens in new window) enter the ordered pair below. ( \boxed{ }, \boxed{ } )

Explanation:

Step1: Solve for y from the first equation

From \( x + y = 6 \), we can express \( y \) as \( y = 6 - x \).

Step2: Substitute y into the second equation

Substitute \( y = 6 - x \) into \( 0.4x + 0.3y = 0.35(6) \).
We get \( 0.4x + 0.3(6 - x) = 2.1 \).

Step3: Simplify and solve for x

First, expand the left - hand side: \( 0.4x+1.8 - 0.3x=2.1 \).
Combine like terms: \( 0.1x+1.8 = 2.1 \).
Subtract 1.8 from both sides: \( 0.1x=2.1 - 1.8=0.3 \).
Divide both sides by 0.1: \( x=\frac{0.3}{0.1}=3 \).

Step4: Solve for y

Substitute \( x = 3 \) into \( y = 6 - x \). Then \( y=6 - 3 = 3 \).

Answer:

\((3, 3)\)