Question

HELP PLEASE!!! 28 POINTS!! 1)A professional pianist spends an average of 45 hours practicing the piano in a three-week period. Using this ratio how many hours does he practice in three months? Set up a proportion, defining a variable for the unknown quantity, solve the proportion, showing all work leading to your answer, and write a sentence to explain the meaning of the answer for the situation.
2) A popular fishing lake contains a combination of largemouth bass and catfish with a ratio of bass to catfish of 10 to 7. If there are 425 bass in the lake, about how many catfish are there? set up a proportion, defining a variable for the unknown quantity, solve the proportion, showing all work leading to your answer, and write a sentence to explain the meaning of the answer for the situation.

Answer 1

Answer:

Part 1) $180\ hours$

Part 2) There are about $298\ catfish$

Step-by-step explanation:

Part 1) we know that

1 month=4 weeks

Let

x------> the number of hours of practice for three months

so

Convert months to weeks

3 months=3(4)=12 weeks

using proportion

$\frac{45}{3}\frac{hours}{weeks} =\frac{x}{12}\frac{hours}{weeks}\\ \\ x=45*12/3\\ \\x=180\ hours$

that means------> In three months (12 weeks) the pianist practice 180 hours

Part 2)

Let

x------> the number of bass

y------> the number of catfish

we know that

Using proportion

$\frac{10}{7}\frac{bass}{catfish} =\frac{425}{y}\frac{bass}{catfish} \\ \\y=425*7/10\\ \\y=297.5\ catfish$

There are about $298\ catfish$