<PRE><B>Question 149606</B>
a contractor has a 24-pound mixture that is no-fourth cement, and three-fourths sand. How much of a mixture that is half cement and half sand needs to be added to produce a mixture that is one-third cement?
:
We can write an equation based on the amt of cement
;
Let x = amt of half cement mixture required
:
{{{1/4}}}(24) + {{{1/2}}}x = {{{1/3}}}(x+24)
Multiply equation by 12 to get rid of the denominators
:
3(24) + 6x = 4(x+24)
:
72 + 6x = 4x + 96
:
6x - 4x = 96 - 72
:
2x = 24
x = {{{24/2}}}
x = 12 lb of the half cement mixture
;
:
we can check solution base on the amt of sand:
{{{3/4}}}(24) + {{{1/2}}}(12) = {{{2/3}}}(12+24)
18 + 6 = {{{2/3}}}*36</PRE>