Question

How much of a spice that is 30% salt should be added to 175 ounces of a spice that is 65% salt in order to make a spice that is 50% salt?

Answer 1

$\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentrated\\ amount \end{array}\\ &-----&-------&-------\\ \textit{30\% spice}&x&0.30&0.30x\\ \textit{65\% spice}&175&0.65&(175)(0.65)\\ -----&-----&-------&-------\\ mixture&x+175&0.50&(x+175)(0.50) \end{array}$

so.. as you can see, we use the decimal notation for the percentages... 65% is just 65/100 and 50% is just 50/100 and so on

so.. whatever the salted amounts are, we know they'll add up to (x+175)(0.50)

thus  (0.30x) + (175)(0.65) = (x+175)(0.50)

solve for "x"