+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?
+9466 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
+9466 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
