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1 Madison is making a vinaigrette for her catering service using.

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1 Madison is making a vinaigrette for her catering service using Olive oil that costs fifty cent per ounce and apple cider vinegar that costs thirty- five cents an ounce. The ideal batch of vinaigrette has 25% vinegar. If she has already combined 3 cups oif vinegar and 1cup of oil, how many cups of oil should she add? What is the total cost of her completed recipe?

Aug 29, 2017

#1
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cups of vinaigrette  =  cups of vinegar + cups of oil

Let's call the amount of additional cups of oil  " x " .

There are   3  cups of vinegar   , and there are   1 + x  cups of oil   in the batch so far.

cups of vinaigrette  =  (3) + (1 + x)

cups of vinaigrette  =  4 + x

We want there to be  25  cups of vinegar for every  100  cups of vinaigrette.   That is....

$$\frac{\text{number of cups of vinegar}}{\text{number of cups of vinaigrette}}=\frac{25}{100}$$       Plug in  3  for cups of vinegar and  4 + x  for cups of vinaigrette.

$$\frac{3}{4+x}\,=\,\frac{25}{100} \\~\\ (4+x)(25)\,=\,(3)(100) \\ 100+25x\,=\,300 \\ 25x\,=\,200 \\ x\,=\,8$$                 Now solve this for  x  . First, let's cross-multiply.

So....she needs to add  8  cups of oil .

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The final recipe will have  9  cups of oil. To find the price, we need to know how many ounces this is.

1 cup    =  8 ounces          Multiply both sides by  9  .

9 cups  =  72 ounces

The final recipe will have  3  cups of vinegar.

1 cup    =  8 ounces

3 cups  =  24 ounces

the total price, in dollars   =   0.50 * (ounces of olive oil)  +  0.35 * (ounces of vinegar)

=   0.50 * 72   +   0.35 * 24

=   36   +   8.4

=   44.40

Aug 29, 2017

#1
+3

cups of vinaigrette  =  cups of vinegar + cups of oil

Let's call the amount of additional cups of oil  " x " .

There are   3  cups of vinegar   , and there are   1 + x  cups of oil   in the batch so far.

cups of vinaigrette  =  (3) + (1 + x)

cups of vinaigrette  =  4 + x

We want there to be  25  cups of vinegar for every  100  cups of vinaigrette.   That is....

$$\frac{\text{number of cups of vinegar}}{\text{number of cups of vinaigrette}}=\frac{25}{100}$$       Plug in  3  for cups of vinegar and  4 + x  for cups of vinaigrette.

$$\frac{3}{4+x}\,=\,\frac{25}{100} \\~\\ (4+x)(25)\,=\,(3)(100) \\ 100+25x\,=\,300 \\ 25x\,=\,200 \\ x\,=\,8$$                 Now solve this for  x  . First, let's cross-multiply.

So....she needs to add  8  cups of oil .

--------------------------------------------------

The final recipe will have  9  cups of oil. To find the price, we need to know how many ounces this is.

1 cup    =  8 ounces          Multiply both sides by  9  .

9 cups  =  72 ounces

The final recipe will have  3  cups of vinegar.

1 cup    =  8 ounces

3 cups  =  24 ounces

the total price, in dollars   =   0.50 * (ounces of olive oil)  +  0.35 * (ounces of vinegar)

=   0.50 * 72   +   0.35 * 24

=   36   +   8.4

=   44.40

hectictar Aug 29, 2017