Question

You have a stock of two blends of dry mix sand and cement that you wish to blend to give you 10 tons at 40% cement content. ?

One of these mixes has 20% cement content and the other has 70% cement content. How many tons of each need to be mixed together to give you the target concentration and weight.

Answer 1

6 tons at 20% blend
4 tons at 70% blend

Explanation:

Target is a blend with 40% cement

Let the amount of 20% material be designated as `M_20`
Let the amount of 70% material be designated as `M_70`

`M_20+M_70=10" "......... .......................Equation(1)`

`20%M_20+70%M_70 = 40%10" "............Equation(2)`

From `Eqn(1)" "M_20=10-M_70" "............Equation(1_a)`

Using `Eqn(1_a)` substitute for `M_20` in `Eqn(2)`

`color(white)("dddddddddd")color(green)(20/100(color(red)(M_20))+70/100M_70=40/100xx10`

`color(white)("dddd")color(white)("dd")20/100(color(red)(10-M_70))+70/100M_70=400/100`

Multiply both sides by 100 to get rid of the fraction

`color(white)("ddddddd")color(white)("dd")20(10-M_70)+70M_70=400`

`color(white)("ddddddddddddd")200color(white)("dddd")+50M_70=400`

`color(white)("dddddddddddddddddddddddd")color(blue)(M_70=(400-200)/50 = 4" tons")`
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Thus `color(blue)(M_20=10-4=6" tons")`

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`color(brown)("Checking LHS - RHS is "40%xx10=4)`

`(20/100xx6)+(70/100xx4) =4`

LHS=RHS thus proven to be true

color(white)("d")