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QuestionTo make 464 liters of Petrolyn oil with a ratio of 5 liters natural to 3 liters synthetic, how much synthetic oil is needed?

Studdy Solution

STEP 1

Assumptions1. Petrolyn motor oil is a combination of natural oil and synthetic oil. . The ratio of natural oil to synthetic oil in Petrolyn motor oil is53.
3. We need to make464 liters of Petrolyn motor oil.

STEP 2

First, we need to understand the ratio of natural oil to synthetic oil in Petrolyn motor oil. The ratio is5, which means for every5 liters of natural oil, there are liters of synthetic oil.This can be written asNatural oilSynthetic oil=5\frac{Natural\, oil}{Synthetic\, oil} = \frac{5}{}

STEP 3

The total amount of Petrolyn motor oil is the sum of the natural oil and synthetic oil.This can be written asTotal Petrolyn oil=Natural oil+Synthetic oilTotal\, Petrolyn\, oil = Natural\, oil + Synthetic\, oil

STEP 4

Substitute the ratio of natural oil to synthetic oil into the equation for total Petrolyn oil.
Total Petrolyn oil=3×Synthetic oil+Synthetic oilTotal\, Petrolyn\, oil = \frac{}{3} \times Synthetic\, oil + Synthetic\, oil

STEP 5

implify the equation by combining like terms.
Total Petrolyn oil=83×Synthetic oilTotal\, Petrolyn\, oil = \frac{8}{3} \times Synthetic\, oil

STEP 6

To find the amount of synthetic oil needed, we rearrange the equation to solve for Synthetic oil.
Synthetic oil=Total Petrolyn oil83Synthetic\, oil = \frac{Total\, Petrolyn\, oil}{\frac{8}{3}}

STEP 7

Plug in the value for the total Petrolyn oil to calculate the amount of synthetic oil needed.
Synthetic oil=4643Synthetic\, oil = \frac{464}{\frac{}{3}}

STEP 8

implify the division by a fraction by multiplying by its reciprocal.
Synthetic oil=464×38Synthetic\, oil =464 \times \frac{3}{8}

STEP 9

Calculate the amount of synthetic oil needed.
Synthetic oil=464×38=174 litersSynthetic\, oil =464 \times \frac{3}{8} =174\, litersTo make464 liters of Petrolyn motor oil,174 liters of synthetic oil are needed.

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