Question 102945: By weight, a 200 ton sample of a certain roadbed material is 75% crushed rock. How many tons of a 30% crushed rock sample must be added to create a mixture that is 50% crushed rock?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the number of tons of 30% crushed required.
To start with, you have 200 tons of 75% crushed rock to which you will add x tons of 30% crushed rock to obtain (200+x) tons of 50% crushed rock.
Now you can write the necessary equation to solve for x.
Change the percentages to their decimal equivalents. (75% = 0.75, 30% = 0.3, and 50% = 0.5)
200(0.75)+x(0.3) = (200+x)(0.5) Simplify and solve for x.
150+0.3x = 100+0.5x Subtract 0.3x from both sides to combine like-terms.
150 = 100+0.2x Now subtract 100 from both sides.
50 = 0.2x Finally, divide both sides by 0.2
250 = x
You will need to add 250 tons of 30% crushed rock to obtain 450 tons of 50% crushed rock.
Check:
200(0.75)+250(0.3) = 450(0.5)
150+75 = 225
225 = 225 OK!
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