# Help

• Mar 5th 2013, 03:54 PM
mbruiz1
Help
The base material for a certain roadbed is 80% crushed rock when measured by weight. How many tons of this material must be mixed with another material containing 30% rock to make 150 tons of material that is 40% crushed rock?
• Mar 5th 2013, 07:32 PM
Soroban
Re: Help
Hello, mbruiz1!

Quote:

The base material for a certain roadbed is 80% crushed rock when measured by weight.
How many tons of this material must be mixed with another material containing 30% crushed rock
to make 150 tons of material that is 40% crushed rock?

Let \$\displaystyle x\$ = tons of 80% material.
This contains \$\displaystyle 0.8x\$ tons of crushed rock.

Let \$\displaystyle 150-x\$ = tons of 30% material.
This contains: \$\displaystyle 0.3(150-x)\$ tons of crushed rock.

The mixture will contain: \$\displaystyle 0.8x + 0.3(150-x)\$ tons of crushed rock.

But we know that the mixture will be 150 tons which is 40% crushed rock.
. . It will contain: \$\displaystyle 0.4(150) \,=\,60\$ tons of crushed rock.

We just described the final amount of crushed rock in two ways.

There is our equaton! . . . \$\displaystyle 0.8x + 0.3(150-x) \;=\;60\$

Got it?