# Ratio Word Problems

### Solutions

1Calculate the unknown term in the following proportions:

1

2

3

4

5

2Anne buys 5 pounds of potatoes at the market. If 2 pounds cost $0.80, how much will Anne pay?

3Calculate the height of a building that casts a shadow of 6.5 meters at the same time that a pole with a height of 4.5 m casts a shadow of 0.90 m.

4The legs of a right triangle measure 24 m and 10 m and its hypotenuse is 26 m. What is the length of the legs of a similar triangle whose hypotenuse is 52 m?

5Two wheels are connected by a transmitter belt. The first has a radius of 25 cm and the second, 75 cm. When the first has reached 300 turns, how many turns will the second have completed?

6Three individuals contribute $5,000, $7,500 and $9,000 which is together invested into a stock. After a year, the stock has made $6,450 on top of the capital. If the money is withdrawn, how much will each individual receive if their earnings are directly proportional to the capital orginally contributed?

## 1

Calculate the unknown term in the following proportions:

1

2

3

4

5

## 2

Anne buys 5 pounds of potatoes at the market. If 2 pounds cost $0.80, how much will Anne pay?

The weight and the price are directly proportional because when the weight increases, the total price increases and when the weight decreases, the total price decreases.

## 3

Calculate the height of a building that casts a shadow of 6.5 meters at the same time, a pole with a height of 4.5 m casts a shadow of 0.90 m.

The height and the length of the shadow are directly proportional because as the height increases, so does the shadows length and as the height decreases, the length of the shadow also decreases.

## 4

The legs of a right triangle measure 24 m and 10 m and its hypotenuse is 26 m. What is the length of the legs of a similar triangle whose hypotenuse is 52 m?

The length of legs are directly proportional to the length of the hypotenuse in the similar triangle. If the hypotenuse inceases, so does the length of the legs and if the length of the hypotenuse decreases, the legs decrease aswell.

## 5

Two wheels are connected by a transmitter belt. The first has a radius of 25 cm and the second, 75 cm. When the first has reached 300 turns, how many turns will the second have completed?

The length of the radius and the number of turns are inversely proportional because the larger the radius is, the fewer times the wheel will complete a rotation and the smaller the radius is, the more frequently the wheel will complete a rotation.

## 6

Three individuals contribute $5,000, $7,500 and $9,000 which is together invested into a stock. After a year, the stock has made $6,450 on top of the capital. If the money is withdrawn, how much will each individual receive if their earnings are directly proportional to the capital orginally contributed?

The amount invested is directly proportional to the amount gained because the more money originally invested translates into a higher return and the less money orginally invested translates into a lower return.