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. ?

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")