Question

How many gallons of a 80% antifreeze solution must be mixed with 100 gallons of 25% antifreeze to get a mixture that is 70% antifreeze?

Answer 1

do you know how to start

Answer 2

No but I know it's a 6 step method

Answer 3

well, we know the amount of 80% of antifreeze will be .. say "x"
the amount of 25% of antifreeze is 100 gallons

and once we mixed them up, that is "x + 100" they should give use a mix that is 70% antifreeze

so \(\begin{array}{llll}
&quantity&percentage&total\ with\ antifreeze
\\\hline\\
80\%\ solution&x&0.8&0.8\cdot {\color{brown}{ x}}\\
25\%\ solution&100&0.25&100\cdot 0.25\\
total\ mixture&{\color{brown}{ x}}+100&0.7&({\color{brown}{ x}}+100)\cdot 0.7
\end{array}\)

so... ahemm, what do you think then?

Answer 4

anyhow \(\begin{array}{llll}
&quantity&percentage&total\ with\ antifreeze
\\\hline\\
80\%\ solution&{\color{brown}{ x}}&0.8&0.8\cdot {\color{brown}{ x}}\\
25\%\ solution&100&0.25&100\cdot 0.25\\
total\ mixture&{\color{brown}{ x}}+100&0.7&({\color{brown}{ x}}+100)\cdot 0.7
\end{array}\)

so... there, do a system of equations, solve by substitution :)

Answer 5

the SUM of the "total with antifreeze" of the 2 solutions, should equate, the mixture's