Question

Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used. What is the value of x? 1 3 10 24

Answer 1

Answer:

10

Step-by-step explanation:

We will use a system of equations to solve this.  We do not know how much of the 25% bleach solution is used; we will use x to represent this.  We know that 5 cups of the 10% solution was used.  We do not know how much of the resulting solution we have; we will use y to represent this.  This gives us the equation

x+5 = y

Using the decimal forms of the percentages for each solution, we have 0.25x (25% solution for x cups), 0.1(5) (10% solution for 5 cups) and 0.2y (20% solution for y cups); this gives us the equation

0.25x+0.1(5) = 0.2y

This gives us the system

$\left \{ {{x+5=y} \atop {0.25x+0.1(5)=0.2y}} \right.$

To use elimination, we will make the coefficients of x the same by multiplying the top equation by 0.25:

$\left \{ {{0.25(x+5=y)} \atop {0.25x+0.5=0.2y}} \right. \\\\\left \{ {{0.25x+1.25=0.25y} \atop {0.25x+0.5=0.2y}} \right.$

We will now subtract the second equation from the first:

$\left \{ {{0.25x+1.25=0.25y} \atop {-(0.25x+0.5=0.2y)}} \right. \\\\0.75 = 0.05y$

Divide both sides by 0.05:

0.75/0.05 = 0.05y/0.05

15 = y

There were 15 cups of the resulting 20% solution.  Substituting this into the first equation, we have

x+5=15

Subtract 5 from each side:

x+5-5=15-5

x = 10

Answer 2

active + active = active

0.25x + 0.10*5 = 0.20(x+5)

25x + 10*5 = 20x + 20*5

5x = 10*5

x = 10 cups (amt. of 25% bleach used)