To determine how many centiliters are in 5 quarts, we'll follow these steps for converting units from quarts to liters, and then from liters to centiliters.
Given:
- 1 quart = 0.95 liters
- 1 liter = 100 centiliters
We need to convert 5 quarts to centiliters. The steps are outlined below:
1. Start with the conversion from quarts to liters:
- We know that 1 quart is equivalent to 0.95 liters.
- Therefore, for 5 quarts:
[tex]\[
5 \text{ quarts} \times 0.95 \text{ liters per quart} = 4.75 \text{ liters}
\][/tex]
2. Convert the resulting liters to centiliters:
- We also know that 1 liter is equivalent to 100 centiliters.
- Using this, convert 4.75 liters to centiliters:
[tex]\[
4.75 \text{ liters} \times 100 \text{ centiliters per liter} = 475 \text{ centiliters}
\][/tex]
For the equation provided in the query:
[tex]\[
\frac{5 \text { quarts }}{1} \times \frac{a}{b} \times \frac{c}{d}=475 \text{ cL}
\][/tex]
we need to identify the values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] such that the conversion products correspond to the correct units.
These values correspond to the unit conversion factors:
- [tex]\(a = 0.95\)[/tex] (since 1 quart is 0.95 liters)
- [tex]\(b = 1\)[/tex] (unit consistency for quarts)
- [tex]\(c = 100\)[/tex] (since 1 liter is 100 centiliters)
- [tex]\(d = 1\)[/tex] (unit consistency for liters)
Thus:
[tex]\[
a = 0.95 \\
b = 1 \\
c = 100 \\
d = 1
\][/tex]
Therefore, the final detailed step-by-step solution and values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] are:
1. Convert quarts to liters:
[tex]\[
5 \text{ quarts} \times 0.95 \text{ liters per quart} = 4.75 \text{ liters}
\][/tex]
2. Convert liters to centiliters:
[tex]\[
4.75 \text{ liters} \times 100 \text{ centiliters per liter} = 475 \text{ centiliters}
\][/tex]
Which gives us:
[tex]\[
a = 0.95 \\
b = 1 \\
c = 100 \\
d = 1
\][/tex]
So, 5 quarts is equivalent to 475 centiliters.
