1. ## 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?

2. ## Re: Help

Hello, mbruiz1!

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?