Question

A 20 pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

Answer 1

`5^("lb")` cement needs to be added

Explanation:

By adding more cement you are increasing the weight. So this needs to be kept in mind.

`25%" of "20^("lb")->1/4xx20=color(green)(5^("lb") larr" original cement content")`

`color(red)("So the amount of sand is "(20-5)^("lb")=15^("lb"))`

We wish to increase the cement such that all of it becomes 40%

That means we will have (100-40)%=60% of the new mix is the original sand content. The mass of which does not change.

Let the new mass of the whole blend be `x^("lb")`

60% of `x=color(red)(" "15^("lb")`

`x=cancel(15)^1xx100/cancel(60)^4 = 25^("lb")larr" Final wieght of the blend"`

`color(purple)("So the added cement is "25-20=5^("lb"))`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

`(color(green)(5+)color(purple)(5))/25 ->10/25->40/100` as required.