Question

a chef is going to use a mixture of two brands of italian dressing. the first brand contains 6% and the second brand contain 11% vinegar. the chef wants to make 220 milliliters of a dressing that is 7% vinegar. how much of each brand should she use

Answer 1

we calculate the vinegar on 220 ml

`\begin{gathered} 220\cdot(7)/(100) \\ =15.4 \end{gathered}`

the dressing will have 15.4 ml of vinegar

now we can raise a sum

`x+y=220`

where X is the first brand and Y the second brand on ml

now the percent vinegar sum we know the result is 15.4 wich corresponds to 7%

`\begin{gathered} x\cdot(6)/(100)+y\cdot(11)/(100)=15.4 \\ \\ 0.06x+0.11y=15.4 \end{gathered}`

we have two unknowns and equations, so we can solve by any method.

i will solve y on the first equation

`\begin{gathered} x+y=220 \\ y=-x+220 \end{gathered}`

and replace on the second to find x

`\begin{gathered} 0.06x+0.11(-x+220)=15.4 \\ 0.06x-0.11x+(121)/(5)=15.4 \\ -(1)/(20)x=15.4-(121)/(5) \\ -(1)/(20)x=-(44)/(5) \\ x=(-44*20)/(5*-1) \\ x=176 \end{gathered}`

then replace x on any equation to solve y

`\begin{gathered} x+y=220 \\ 176+y=220 \\ y=44 \end{gathered}`

for each brand should she use x=176ml and y=44ml