An engineer wants to make a 60% cement mixture. how many pounds of an 80% cement mixture must she mix with 14 pounds of a 50% mixture to create a 60% cement mixture?

In 14 pounds of a 50% mixture we have 0.5*14=7pounds of cement
lets think that we need x pounds of mix of an 80% cement so in that mix we will have 0.8x pounds of cement. If we'll mix both we wiil have (14+x)pounds of mix and  we have (0.8x+7) cement on it.

in mixture mix there are 60% of (x+14)pounds of cement so it is 0.6(x+14) of cement

make equation (sum of mix)
0.6(x+14)=0.8x+7
0.6x+8.4=0.8x+7
0.2x=1.4
x=7

engineer need 7pounds of 80% mix

P.s. look at the picture it more easy for understanding!

The method to find the female dormitory is 2-d=800