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QuestionSolve for yy in the equation 0.10(50)+0.20y=0.18(50+y)0.10(50) + 0.20y = 0.18(50+y) to find the volume of the 20%20\% solution needed.

Studdy Solution

STEP 1

Assumptions1. The volume of the10% saltwater solution is represented by x. . The volume of the20% saltwater solution is represented by y.
3. The final solution is an18% saltwater solution.
4. The equation0.10x +0.20y =0.18(x + y) represents this situation.
5. We are given that x =50 gallons.

STEP 2

First, we will substitute the given value of x into the equation.
0.10⋅50+0.20y=0.18(50+y)0.10 \cdot50 +0.20y =0.18(50 + y)

STEP 3

implify the left side of the equation.
5+0.20y=0.18(50+y)5 +0.20y =0.18(50 + y)

STEP 4

Expand the right side of the equation.
+0.20y=9+0.18y +0.20y =9 +0.18y

STEP 5

Subtract0.18y from both sides of the equation to isolate the y term on one side.
5+0.20y−0.18y=95 +0.20y -0.18y =9

STEP 6

implify the left side of the equation.
5+0.02y=95 +0.02y =9

STEP 7

Subtract5 from both sides of the equation to isolate the y term.
0.02y=9−50.02y =9 -5

STEP 8

implify the right side of the equation.
0.02y=40.02y =4

STEP 9

Divide both sides of the equation by.02 to solve for y.
y=4/.02y =4 /.02

STEP 10

Calculate the value of y.
y=4/0.02=200y =4 /0.02 =200So,200 gallons of the20% saltwater solution will be needed if50 gallons of the10% saltwater solution is used.

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