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.
Answers
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
{use a+5=y 0.25x+0.1(5)=0.24
To use elimination, we will make the coefficients of x the same by multiplying the top equation by 0.25:
0.25(x + 5 = y)
0.25x + 0.5 = 0.2y
(0.25x + 1.25 = 0.25y
| 0.25x + 0.5 = 0.2y
We will now subtract the second equation from the first:
10.25x + 0.5 = 0.2y
(0.25x + 1.25 = 0.25%
0.25x + 0.5 = 0.2y
We will now subtract the second from the first:
( 0.25x + 1.25 0.25y {
(0.25x + 0.5 = 0.2y)
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