+0

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

0
152
1
+171

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?

BOSEOK  Aug 29, 2017

#1
+5931
+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
Sort:

#1
+5931
+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

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details