QuestionThe volumes of bottles $A$ , $B$ , and $C$ are in the ratio $8:15:6$ . If $C = 450 \mathrm{~mL}$ , find the total volume.

Studdy Solution

STEP 1

Assumptions1. The volumes of the three bottles of juice, A, B and C, are in the ratio8156. The volume of bottle C is450 mL3. The total volume is the sum of the volumes of all three bottles

STEP 2

First, we need to find the total parts in the ratio. We can do this by adding the ratio parts together.
$Total\, parts = A\, parts + B\, parts + C\, parts$

STEP 3

Now, plug in the given values for the parts of A, B and C to calculate the total parts.
$Total\, parts =8 +15 +6$

STEP 4

Calculate the total parts.
$Total\, parts =8 +15 +6 =29$

STEP 5

Now that we have the total parts, we can find the volume of one part. This can be done by dividing the volume of C by the number of parts for C.
$Volume\, of\, one\, part = Volume\, of\, C / C\, parts$

STEP 6

Plug in the values for the volume of C and the parts of C to calculate the volume of one part.
$Volume\, of\, one\, part =450\, mL /6$

STEP 7

Calculate the volume of one part.
$Volume\, of\, one\, part =450\, mL /6 =75\, mL$

STEP 8

Now that we have the volume of one part, we can find the total volume of the three bottles. This can be done by multiplying the total parts by the volume of one part.
$Total\, volume = Total\, parts \\times Volume\, of\, one\, part$

STEP 9

Plug in the values for the total parts and the volume of one part to calculate the total volume.
$Total\, volume =29 \\times75\, mL$

STEP 10

Calculate the total volume.
$Total\, volume =29 \\times75\, mL =2175\, mL$ The total volume of the three bottles of juice is2175 mL.

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