QuestionTo make 532 liters of Petrolyn oil, how many liters of synthetic oil are needed if the ratio is 4 liters natural to 3 liters synthetic?

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 is43.
3. The total amount of Petrolyn oil to be made is532 liters.

STEP 2

First, we need to find the total parts in the Petrolyn oil. This can be done by adding the parts of natural oil and synthetic oil.
$Total\, parts = Parts\, of\, natural\, oil + Parts\, of\, synthetic\, oil$

STEP 3

Now, plug in the given values for the parts of natural oil and synthetic oil to calculate the total parts.
$Total\, parts = +3$

STEP 4

Calculate the total parts in the Petrolyn oil.
$Total\, parts =4 +3 =7$

STEP 5

Now that we have the total parts, we can find out how many liters each part represents. This can be done by dividing the total amount of Petrolyn oil by the total parts.
$Liters\, per\, part = Total\, amount\, of\, Petrolyn\, oil / Total\, parts$

STEP 6

Plug in the values for the total amount of Petrolyn oil and the total parts to calculate the liters per part.
$Liters\, per\, part =532\, liters /$

STEP 7

Calculate the liters each part represents.
$Liters\, per\, part =532\, liters /7 =76\, liters$

STEP 8

Now that we have the liters each part represents, we can find out how many liters of synthetic oil are needed. This can be done by multiplying the liters per part by the parts of synthetic oil.
$Liters\, of\, synthetic\, oil = Liters\, per\, part \\times Parts\, of\, synthetic\, oil$

STEP 9

Plug in the values for the liters per part and the parts of synthetic oil to calculate the liters of synthetic oil.
$Liters\, of\, synthetic\, oil =76\, liters \\times3$

STEP 10

Calculate the liters of synthetic oil needed.
$Liters\, of\, synthetic\, oil =76\, liters \\times3 =228\, liters$ So,228 liters of synthetic oil are needed to make532 liters of Petrolyn oil.

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