solution word problem
A scientist wants to dilute a 60% acid solution by adding some 20% solution. If she starts with 80 ml of the 60% solution, how many milliliters of the 20% solution does she need to add to get a resulting 45% acid solution?
Let x be the amount of the 60% solution
Let y be the amount of the 20% solution
Let x + y be the amount of the mixture
60% of x solution + 20% of y solution = 45% of amount of mixture
We use 60% of the x solution or 60% of 80 ml.
60% of 80 = 0.60 times 80 = 48
We use 20% of the y solution or 20% of y
20% of y = 0.20 times y = 0.20y
The mixture is x + y and we need 45% of the mixture or
45% of (x + y)
45% of (x + y) = 0.45(x + y)
Putting it all together we get:
48 + 0.20y = 0.45(48 + y)
48 + 0.20y = 21.6 + 0.45y
48 - 21.6 = 0.45y - 0.20y
26.4 = 0.25y
y = 26.4 / 0.25 = 105.6
0.60 times 80 + 0.20 times 105.6 = 48 + 21.12 = 69.12
0.45 times (48 + 105.6) = 0.45 times 153.6 = 69.12
Click here to post comments
Join in and write your own page! It's easy to do. How? Simply click here to return to System of linear equations.
Jan 20, 20 01:57 PM
Top-notch information for those who want to become a high school math teacher. All important stuff that you need to know before making a move can be found right here on this website.
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.