5.5 Application ii - solving problems  (Page 3/4)

The radius of the sun is about 695,202 km (kilometers). That is about 109 times as big as the radius of the Earth. What is the radius of the earth?

5. The radius of the earth is km.

The perimeter of a triangle is 105 cm. If each of the two legs is exactly twice the length of the base, how long is each leg?

1. Let $x=$
                Draw a picture.
5. Each leg is cm long. The base is .

A lumber company has contracted to cut boards into two pieces so that one piece is three times the length of the other piece. If a board is 12 feet long, what is the length of each piece after cutting?

5. The length of the shorter piece is feet, and the length of the longer piece is feet.

A student doing a chemistry experiment has a beaker that contains 84 ml (milliliters) of an alcohol and water solution. Her lab directions tell her that there is $4.6$ times as much water as alcohol in the solution. How many milliliters of alcohol are in the solution? How many milliliters of water?

5. There are ml of alcohol in the solution. There are ml of water in the solution.

A statistician is collecting data to help him estimate the average income of accountants in California. He needs to collect 390 pieces of data and he is $\frac{\text{2}}{\text{3}}$ done. How many pieces of data has the statistician collected?

5. The statistician has collected pieces of data.
   Suppose the statistician is 4 pieces of data short of being $\frac{\text{2}}{\text{3}}$ done. How many pieces of data has he collected?

A television commercial advertises that a certain type of battery will last, on the average, 20 hours longer than twice the life of another type of battery. If consumer tests show that the advertised battery lasts 725 hours, how many hours must the other type of battery last for the advertiser’s claim to be valid?

5. The other type of battery must last hours for the advertiser’s claim to be valid.

A 1000-ml flask containing a chloride solution will fill 3 beakers of the same size with 210 ml of the solution left over. How many milliliters of the chloride solution will each beaker hold?

5. Each beaker will hold ml of the chloride solution.

A star burns $\frac{\text{2}}{\text{9}}$ of its original mass then blows off $\frac{\text{3}}{\text{7}}$ of the remaining mass as a planetary nebula. If the final mass is 3 units of mass, what was the original mass?

5. The original mass was units of mass.

The sum of a number and sixteen is forty-two. What is the number?

When eleven is subtracted from a number, the result is 85. What is the number?

Three times a number is divided by 6 and the result is $\text{10}\text{.5}$ . What is the number?

When a number is multiplied by itself, the result is 144. What is the number?

A number is tripled, then increased by seven. The result is 48. What is the number?

Eight times a number is decreased by three times the number, giving a difference of 22. What is the number?